Question 15 Marks
A shopkeeper allows $20\%$ discount on his article. What price must be mark on an article, which costs him $Rs.1750,$ to make a profit $20\%\ ?$
AnswerLet the marked price be $Rs. x$
Discount$=20 \% $
$\therefore \text { S.P. }=\text { M.P. }- $ discount
$=x-20 \%$ of $\text { Rs. } x $
$=\text { Rs. } \frac{80}{100} x$
Given, $C.P. = Rs. 1750$
Gain$=20 \% $
$\frac{\text { S.P. }}{\text { C.P }}=1+\frac{\text { Gain }}{100} $
$\Rightarrow \frac{\frac{80}{100} x}{1750}=1+\frac{20}{100} $
$\Rightarrow x =\left(\frac{120}{100}\right) \times 1750 \times \frac{100}{80} $
$=\text { Rs. } 2625$
$\therefore$ The marked price $= Rs. 2625 .$
View full question & answer→Question 25 Marks
A tradesman sells his goods at $10\%$ discount. What price should he mark on an article that costs him $Rs.2400,$ to gain $12.5\%$
AnswerLet the marked price be $Rs. x$
Discount $=10 \% $
$\therefore S . P .=\text { M.P. }-$ discount
$=x-10 \%$ of $\text {Rs. } x$
$=\text { Rs. } \frac{90}{100} x$
Given, $C.P.= Rs. 2400$
Gain$=12.5 \%$
$\frac{\text { S.P. }}{\text { C.P }}=1+\frac{\text { Gain }}{100} $
$\Rightarrow \frac{\frac{90}{100} x}{2400}=1+\frac{12.5}{100} $
$\Rightarrow x =\left(\frac{112.5}{100}\right) \times 2400 \times \frac{100}{90}$
$=\text { Rs.3000 } $
$\therefore$ The marked price$=\text { Rs. } 3000 .$
View full question & answer→Question 35 Marks
Two dealers $A$ and $B$ selling the same model of refrigerator mark them under the same selling price. $A$ gives successive discount of $25\%$ and $5\%$ and $B$ gives successive discounts of $10\%$ and $20\%.$ From whom is it more advantageous to purchase the refrigerator?
AnswerLet the marked price be $Rs. 100$
For dealer $A$,successive discounts$=25 \%, 5 \%$
$\text { S.P. }=\left(1-\frac{D_1}{100}\right)\left(1-\frac{D_2}{100}\right) \text { M.P. } $
$=\left(1-\frac{25}{100}\right)\left(1-\frac{5}{100}\right) 100$
$=\frac{75}{100} \times \frac{95}{100} \times 100 $
$=\text { Rs. } 71.25$
Total discount
$=\text { Rs. } 100-\text { Rs. } 71.25 $
$=\text { Rs. } 28.50$
For dealer $B_{\text {, }}$ successive discounts $=10 \%, 20 \%$
$\text { S.P. }=\left(1-\frac{D_1}{100}\right)\left(1-\frac{D_2}{100}\right) \text { M.P. } $
$=\left(1-\frac{10}{100}\right)\left(1-\frac{20}{100}\right) 100 $
$=\frac{90}{100} \times \frac{80}{100} \times 100 $
$=\text { Rs. } 72$
Total discount
$=\text { Rs. } 100-\text { Rs. } 72$
$=\text { Rs. } 28$
$\therefore$ Discount from dealer $A$ is better.
View full question & answer→Question 45 Marks
The printed price of a book is $Rs.320. A$ retailer pays $Rs.244.80$ for it. He gets successive discounts of $10\%$ and another rate. what is the second rate?
Answer$M.P.$ of the book $= Rs. 320$
$S.P.$ of the book $= Rs. 244.80$
Let the second rate of discount be $D$
$\text { S.P. }=\left(1-\frac{D_1}{100}\right)\left(1-\frac{D_2}{100}\right) \text { M.P. } $
$\Rightarrow 244.80=\left(1-\frac{10}{100}\right)\left(1-\frac{D}{100}\right) 320 $
$\Rightarrow 244.80=\frac{90}{100} \times\left(1-\frac{D}{100}\right) \times 320 $
$\Rightarrow\left(1-\frac{D}{100}\right)=\frac{244.80 \times 100}{90 \times 320}=0.85 $
$\Rightarrow \frac{D}{100} $
$=1-0.85 $
$=0.15 $
$\Rightarrow D=15 \%$
$\therefore$ The second rate is $15 \%$.
View full question & answer→Question 55 Marks
A retailer buys a washing machine marked at $Rs.4800$ and gets two successive discounts of $15\%$ and $5\%.$ He spends $Rs.124$ on transportation and sells it at a gain of $13\%.$ Find the selling price of the machine.
Answer$M.P.$ of the machine $= Rs. 4800$
Successive discounts,
$D_1=15 \% $
$D_2=5 \% $
$\text { S.P. }=\left(1-\frac{D_1}{100}\right)\left(1-\frac{D_2}{100}\right) \text { M.P. } $
$=\left(1-\frac{15}{100}\right)\left(1-\frac{5}{100}\right) 4800 $
$=\frac{85}{100} \times \frac{95}{100} \times 4800 $
$=\text { Rs. } 3876$
Transportation $= Rs. 124$
$\therefore C.P$. for the retailer
$=\text { Rs. } 3876+\text { Rs. } 124 $
$=\text { Rs. } 4000$
Gain
$=13 \%$ of $\text {Rs. } 4000$
$=\text { Rs. } 520 $
$\therefore \text { S.P. } $
$=\text { C.P.} + $ Gain
$=\text { Rs. } 4000+\text { Rs. } 520 $
$=\text { Rs. } 4520$
$\therefore$ The selling price of the machine $=\operatorname{Rs.4520}$.
View full question & answer→Question 65 Marks
The difference between a discount of $30\%$ and two successive discounts of $20\%$ and $10\%$ is $Rs.144.$ Find the list price of the article.
AnswerLet the list price be $Rs. 100$
In the first case, discount $=30 \%$
$\text { S.P. }=\text { M.P. }-$ discount
$=\text { Rs. } 100-30 \% \text { of Rs. } 100 $
$=\text { Rs. } 70$
In the second case, successive discounts $=20 \%, 10 \%$
$\text { S.P. }=\left(1-\frac{D_1}{100}\right)\left(1-\frac{D_2}{100}\right) \text { M.P. } $
$=\left(1-\frac{20}{100}\right)\left(1-\frac{10}{100}\right) 100 $
$=\frac{80}{100} \times \frac{90}{100} \times 100 $
$=\text { Rs. } 72$
$\therefore$ Difference between the $S.P.$
$=\text { Rs. } 72-\text { Rs. } 70 $
$=\text { Rs. } 2$
When difference is $Rs.2$,
$M.P. = Rs. 100$
When differences is $Rs. 144 ,$
$M.P.=\frac{100 \times 144}{2} $
$=\text { Rs. } 7200$
$\therefore$ The list price of the article is $Rs. 7200 .$
View full question & answer→Question 75 Marks
First the difference between a single discount of $40\%$ and two successive discounts of $36\%$ and $4\%$ on $Rs.5000.$
Answer$\text { M.P. }=\text { Rs. } 5000$
In First case, discount$=40 \% $
$ \frac{\text { S.P. }}{\text { M.P. }}=1-\frac{\text { discount }}{100} $
$ \Rightarrow \frac{\text { S.P. }}{5000}=1-\frac{40}{100} $
$ \Rightarrow \text { S.P. }=\frac{60}{100} \times \text { Rs. } 5000 $
$=\text { Rs. } 3000$
In Second case, successive discounts$=36 \%, 4 \% $
$ \text { S.P. }=\left(1-\frac{D_1}{100}\right)\left(1-\frac{D_2}{100}\right) \text { M.P. } $
$=\left(1-\frac{36}{100}\right)\left(1-\frac{4}{100}\right) 5000$
$=\frac{6}{100} \times \frac{96}{100} \times 5000$
$=\text { Rs. } 3072$
$\therefore$ Difference between both the $S.P.'s $
$ =\text { Rs. } 3072-\text { Rs. } 3000$
$=\text { Rs. } 72 .$
View full question & answer→Question 85 Marks
The catalogue price of an article is $Rs.3600$ and a manufacturer sells it to the distributor at $20\%$ off the catalogue price. The distributor sells it to the retailer at $10\%$ off the catalogue price. What profit percent is made by the retailer, if he sells the article to a customer at catalogue price? What profit percent is made by the manufacturer, if the catalogue price is $44\%$ above its costs?
Answer$M.P.$ of the article $= Rs. 3600$
For the distributor, $C.P.$
$= Rs. 3600-20 \%$ of $Rs. 3600$
$= Rs. 3600-R s .720$
$= Rs. 2880$
$S.P.$
$= Rs.3600-10 \%$ of $Rs. 3600$
$=Rs.3600-R s .360$
$= Rs. 3240$
For the retailer,
$C.P. = Rs. 3240$
$S.P. =Rs=3600$
$\therefore$ Gain
$= S.P. - C.P.$
$=R s .3600-R s .3240$
$=Rs. 360$
$\therefore$ Gain $\%$
$=\frac{\text { gain }}{\text { C.P. }} \times 100$
$=\frac{360}{3240} \times 100$
$=11.1 \%$
If catalogue price is $44 \%$ above its costs, then
$\frac{\text { M.P. }}{\text { C.P. }}=1+\frac{44}{100}$
$\Rightarrow \frac{3600}{\text { C.P. }}=\frac{144}{100}$
$\Rightarrow$ C.P. $=\frac{100 \times 3600}{144}$
$= Rs. 2500$
$S.P.$ for the manufacturer
$= M.P. -$ Discount
$=Rs. 3600-20 \%$ of $Rs. 3600$
$=Rs. 3600-R s .720$
$= Rs. 2880$
Gain
$= S.P. - C.P.$
$=Rs. 2880 - Rs. 2500$
$=Rs. 380$
$\therefore$ Gain $\%$
$=\frac{\text { gain }}{\text { C.P. }} \times 100$
$=\frac{380^{\circ}}{2500} \times 100$
$=15.2 \%$.
View full question & answer→Question 95 Marks
The catalogue price of a Sony $TV$ is $Rs.43200.$ If it is sold at a discount of $16\%$ of the catalogue price, a gain of $26\%$ is made. Find the gain or loss percent if it is sold for $Rs.9000$ below the catalogue price.
AnswerGiven, $M.P.$ of the $TV = Rs. 43200$
Discount $=16 \%$
$\frac{\text { S.P. }}{\text { M.P. }}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\text { S.P. }}{43200}=1-\frac{16}{100} $
$\Rightarrow \text { S.P. }=\frac{84}{100} \times \text { Rs. } 43200 $
$=\text { Rs. } 36288 $
Gain $=26 \% $
$\frac{\text { S.P. }}{\text { C.P }}=1+\frac{\text { gain }}{100} $
$\Rightarrow \frac{36288}{\text { C.P. }}=1+\frac{26}{100} $
$\Rightarrow \text { C.P. }=\frac{100}{126} \times \text { Rs. } 36288 $
$=\text { Rs. } 28800$
New $S.P.$
$=\text { Rs. } 43200-R s .9000 $
$=\text { Rs. } 34200 $
Gain
$=\text { Rs. } 34200-R s .28800 $
$=\text { Rs. } 5400 $
$\therefore$ Gain $\% $
$=\frac{\text { gain }}{\text { C.P. }} \times 100 $
$=\frac{5400}{28800} \times 100 $
$=18.75 \% .$
View full question & answer→Question 105 Marks
A publisher gives his distributors a discount of $30\%$ on the printed price of the books. The distributor sells those books to a book seller at $23\%$ discount on the printed price and the book$-$seller sells these books at their printed price. Find the profit percent made by the distributor and the book$-$seller.
AnswerLet the printed price of the books $= Rs. 100$
Discount given by publisher
$=30 \%$ of $Rs. 100$
$=\frac{30}{100} \times 100$
$=\text { Rs. } 30$
$\therefore$ Selling Price of publisher
$=$ Printed price $-$ Discount
$= Rs. 100- Rs. 30$
$= Rs .70$
Cost price to distributor $= Rs. 70$
Now, discount given by distributor
$=23 \%$ of $Rs. 100$
$=\frac{23}{100} \times 100$
$=\text { Rs. } 23$
$\therefore$ Selling Price of distributor
$=$ Printed price $-$ Discount
$=\text { Rs. } 100-\text { Rs. } 23$
$=\text { Rs. } 77$
Cost price of bookseller $= Rs. 77$
$S.P. $of book seller $=Rs. 100$
Profit made by bookseller
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. }(100-77)$
$=\text { Rs. } 23$
Profit made by distributor
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. }(77-70)$
$=\text { Rs. } 7$
Now, profit $\%$ made by distributor
$=\frac{\text { Profit }}{\text { C.P. }} \times 100$
$=\frac{7}{70} \times 100$
$=10 \%$
Profit $\%$ made by seller
$=\frac{\text { Profit }}{\text { C.P. }} \times 100$
$=\frac{23}{77} \times 100$
$= Rs.29.8\%.$
View full question & answer→Question 115 Marks
A shopkeeper allows $20\%$ discount on the advertised prices of his goods and still makes a profit of $12\%$ on his cost price. Calculate the advertised price of an article on which he gains $Rs.135.$
AnswerLet the $C.P.$ of the goods $= Rs. 100$
Profit $=12 \%$
$\therefore S.P.$
$=Rs. 100+12 \%$ of $Rs. 100$
$=Rs.100+ Rs. 12$
$= Rs. 112$
Discount $=20 \%$
$\frac{\text { S.P. }}{\text { M.P. }}=1-\frac{D}{100}$
$\Rightarrow \frac{112}{\text { M.P. }}=1-\frac{20}{100}$
$\Rightarrow M.P. =\frac{112 \times 100}{80}$
$= Rs. 140$
Gain
$=S.P. - C.P.$
$=Rs. (112-100)$
$= Rs. 12$
When gain is $Rs. 12, M.P. = Rs. 140$
When gain is $Rs. 135,$
$M.P.=\frac{140 \times 135}{12}$
$=\text { Rs. } 1575 .$
View full question & answer→Question 125 Marks
A dealer marks his goods $25\%$ above the cost price and then allows $10\%$ discount on it. What is the cost price of an article on which he gains $Rs.575$?
AnswerLet the $C.P$. of the goods $= Rs. 100$
$\therefore \text { M.P. }$
$=\text { Rs. } 100+25 \%$ of $\text {Rs. } 100$
$=\text { Rs. } 100+\text { Rs. } 25$
$=\text { Rs. } 125$
Discount
$=10 \%$ of $\text {Rs. } 125$
$=\frac{10}{100} \times 125$
$=\text { Rs. } 12.5$
$\therefore \text { S.P. }$
$=\text { M.P. }-$ Discount
$=\text { Rs. }(125-12.5)$
$=\text { Rs. } 112.5$
Gain
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. }(112.5-100)$
$=\text { Rs. } 12.5$
When gain is $Rs. 12.5, C . P .=R s .100$
When gain is $Rs. 575,$
$C.P.=\frac{100 \times 575}{12.5}$
$=\text { Rs. } 4600 .$
View full question & answer→Question 135 Marks
A dealer marks his goods $45\%$ above the cost price and then allows $20\%$ discount on it. What is the cost price of an article on which he gains $Rs.960$?
AnswerLet the $C.P.$ of the goods $= Rs. 100$
$\therefore M.P.$
$=Rs.100+45 \%$ of $Rs. 100$
$=R s .100+R s .45$
$= Rs. 145$
Discount
$=20 \%$ of $Rs. 145$
$=\frac{20}{100} \times 145$
$=Rs. 29$
$\therefore S . P$.
$=M.P. -$Discount
$=Rs. (145-29)$
$= Rs. 116$
Gain
$=S . P .-C . P$.
$=Rs.(116-100)$
$=Rs. 116$
Gain
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. }(116-100)$
$=\text { Rs. } 16$
When gain is $Rs. 16,$
$ C . P .=R s .100$
When gain is $Rs.960, $
$C.P=\frac{100 \times 960}{16}$
$=\text { Rs. } 6000 .$
View full question & answer→Question 145 Marks
A trader allows a discount of $15\%$ on the marked price of the goods in his shop. However, he still makes a gross profit of $36\%$ on the cost price. Find the profit percent, he would have made, had he sold the goods at the market price.
AnswerLet the cost price of the goods $= Rs. 100$
Profit
$=36 \%$ of $\text {Rs. } 100 $
$=\text { Rs. } 36 $
$\therefore \text { S.P. } $
$=\text { C.P. }+$Profit
$=\text { Rs. }(100+36) $
$=\text { Rs. } 136$
Discount $=15 \%$
$\frac{\text { S.P. }}{\text { M.P }}=1-\frac{D}{100}$
$\Rightarrow \frac{136}{\text { M.P. }}=1-\frac{15}{100} $
$\Rightarrow \frac{136}{\text { M.P. }}=\frac{85}{100} $
$\Rightarrow \text { M.P. }=\frac{100 \times 136}{85} $
$=\text { Rs. } 160$
Profit
$=\text { M.P. }- \text { C.P. } $
$=\text { Rs. }(160-100) $
$=\text { Rs. } 60$
Profit $\%=60 \%$
He would have made a profit of $60 \%$ by selling at the market price.
View full question & answer→Question 155 Marks
A trader allows a discount of $12\%$ on the marked price of the goods in his shop. He still makes a gross profit of $21\%$ on the cost price. Find the profit percent, he would have made, had he sold the goods at the marked price.
AnswerLet the cost price of the goods $= Rs. 100$
Profit
$=21 \%$ of $\text {Rs. } 100 $
$=\text { Rs. } 21 $
$\therefore \text { S.P. } $
$=\text { C.P. }+$Profit
$=\text { Rs. }(100+21) $
$=\text { Rs. } 121$
Discount $=12 \%$
$\frac{\text { S.P. }}{\text { M.P. }}=1-\frac{D}{100} $
$\Rightarrow \frac{121}{\text { M.P. }}=1-\frac{12}{100} $
$\Rightarrow \frac{121}{\text { M.P. }}=\frac{88}{100} $
$\Rightarrow \text { "M.P." }=\frac{100 \times 121}{100} $
$=\text { Rs. } 137.5$
Profit
$=\text { M.P. }- \text { C.P. } $
$=\text { Rs. }(137.5-100) $
$=\text { Rs. } 37.5$
Profit $\%=37.5 \%$
He would have made a profit of $37.5 \%$ by selling at the market price.
View full question & answer→Question 165 Marks
A trademan fixed the selling price of his goods at $40\%$ above the cost price. He sells half his goods at this price, one$-$forth of his stock at a discount of $15\%$ om the original selling price, and the rest at a discount of $25\%$ on the original selling price. Find the gain percent altogether
AnswerLet the $C.P.$ of each article bought $= Rs. 100$
Let the number of articles bought $=x$
$\therefore C.P.$ of the articles $= Rs. 100 x$
$M.P.$of the articles
$=\text { Rs. } 100+40 \%$ of $\text {Rs. } 100$
$=\text { Rs. } 140$
Stage $1:$
No. of articles sold at $Rs. 140=\frac{x}{2}$
$\therefore \text { S.P. of } \frac{x}{2} \text { articles }$
$=\text { Rs. }\left(140 \times \frac{x}{2}\right)$
$=\text { Rs. } 70 x$
Stage $2 :$
Discount
$=15 \%$ of $\text {Rs. } 140$
$=\frac{15}{100} \times \text { Rs. } 140$
$=\text { Rs. } 21$
$\therefore S.P.$
$=Rs.140-Rs. 21$
$= Rs. 119$
No. of articles sold at $Rs. 119=\frac{x}{4}$
$\therefore S.P.$ of $\frac{x}{4}$ articles
$=Rs.\left(119 \times \frac{x}{4}\right)$
$=Rs. 29.75 x$
Stage $3 :$
Discount
$=25 \%$ of $Rs. 140$
$=\frac{25}{100} \times Rs. 140$
$= Rs. 35$
$\therefore S.P.$
$=Rs. 140-R s .35$
$= Rs. 105$
No. of articles sold at $Rs. 90=\frac{x}{4}$
$\therefore S.P.$ of $\frac{x}{4}$ articles
$=Rs.\left(105 \times \frac{x}{4}\right)$
$=Rs. 26.25 x$
Total $S.P. $ of all articles
$=R s .70 x+R s .29 .75 x+R s .26 .25 x$
$=Rs. 126 x$
$\because S . P,>C . P$,
$ \therefore$ there is a gain
Gain
$=\text { Rs. } 126 x-\text { Rs. } 100 x$
$=\text { Rs. } 26 x$
Gain $\%$
$=\frac{\text { gain }}{\text { C.P. }} \times 100$
$=\frac{26 x}{100 x} \times 100$
$=26 \% .$
View full question & answer→Question 175 Marks
A man fixes the selling price of his goods at $50\%$ above the cost price. He sells one$-$third of his stock at this price, one$-$third of his stock at a discount of $20\%$ on the original selling price, and the rest at a discount of $40\%$ on the original selling price. Find the gain percent altogether.
AnswerLet the $C.P.$ of each article bought $= Rs. 100$
Let the number of articles bought $=x$
$\therefore C.P.$ of the articles $= Rs. 100 x$
$M.P.$ of the articles
$=\text { Rs. } 100+50 \%$ of $\text {Rs. } 100$
$=\text { Rs. } 150$
Stage $1:$
No. of articles sold at $Rs. 150=\frac{x}{3}$
$\therefore S.P.$ of $\frac{x}{3}$ articles
$=\text { Rs. }\left(150 \times \frac{x}{3}\right)$
$=\text { Rs. } 50 x$
Stage $2 :$
Discount
$=20 \%$ of $\text {Rs. } 150$
$=\frac{20}{100} \times \text { Rs. } 150$
$=\text { Rs. } 30$
$\therefore \text { S.P. }$
$=\text { Rs. } 150-\text { Rs. } 30$
$=\text { Rs. } 120$
No. of articles sold at $Rs. 120=\frac{x}{3}$
$\therefore \text { S.P.}$ of $\frac{x}{3} \text { articles }$
$=\text { Rs. }\left(120 \times \frac{x}{3}\right)$
$=\text { Rs. } 40 x$
Stage $3 :$
Discount
$=40 \%$ of $\text {Rs. } 150$
$=\frac{40}{100} \times \text { Rs. } 150$
$=\text { Rs. } 60$
$\therefore \text { S.P. }$
$=\text { Rs. } 150-\text { Rs. } 60$
$=\text { Rs. } 90$
No. of articles sold at $Rs.90=\frac{x}{3}$
$\therefore \text { S.P.}$ of $\frac{x}{3}$ articles
$=\text { Rs. }\left(90 \times \frac{x}{3}\right)$
$=\text { Rs. } 30 x$
Total $S.P.$ of all articles
$=\text { Rs. } 50 x +\text { Rs. } 40 x +\text { Rs. } 30 x$
$=\text { Rs. } 120 x$
$\because S . P .>C . P$, therefore there is a gain
Gain
$=\text { Rs. } 120 x-\text { Rs. } 100 x$
$=\text { Rs. } 20 x$
Gain $\%$
$=\frac{\text { gain }}{\text { C.P. }} \times 100$
$=\frac{20 x}{100 x} \times 100$
$=20 \% .$
View full question & answer→Question 185 Marks
A shopkeeper fixes the selling price of his goods at $60\%$ above the cost price. He sells half of his stock at this price, a quarter of his stock at a discount of $25\%$ on the original selling price, and the rest at a discount of $50\%$ on the original selling price. Find the gain percent altogether.
AnswerLet the $C.P.$ of each article bought $=Rs. 100$
Let the number of articles bought $=x$
$\therefore C . P$. of the articles $=Rs. 100 x$
$M.P.$ of the articles
$=Rs.100+60 \%$ of $Rs. 100$
$=Rs. 160$
Stage $1:$
No. of articles sold at $Rs.160=\frac{x}{2}$
$\therefore S.P.$ of $\frac{x}{2}$ articles
$=Rs.\left(160 \times \frac{x}{2}\right)$
$= Rs .80 x$
Stage $2 :$
Discount
$=25 \%$ of $\text {Rs. } 160$
$=\frac{25}{100} \times \text { Rs. } 160$
$=\text { Rs. } 40$
$\therefore \text { S.P. }$
$=\text { Rs. } 160-\text { Rs. } 40$
$=\text { Rs. } 120$
No. of articles sold at $Rs. 120=\frac{x}{4}$
$\therefore S.P$ . of $\frac{x}{4}$ articles
$=Rs.\left(120 \times \frac{x}{4}\right)$
$=\text { Rs. } 30 x$
Stage $3 :$
Discount
$=50 \%$ of $\text {Rs. } 160$
$=\frac{50}{100} \times \text { Rs. } 160$
$=\text { Rs. } 80$
$\therefore \text { S.P. }$
$=\text { Rs. } 160-\text { Rs. } 80$
$=\text { Rs. } 80$
No. of articles sold at $Rs. 80=\frac{x}{4}$
$\therefore S.P.$ of $\frac{x}{4}$ articles
$=Rs. \left(80 \times \frac{x}{4}\right)$
$=Rs. 20 x$
Total $S.P.$ of all articles
$=\text { Rs. } 80 x +\text { Rs. } 30 x +\text { Rs. } 20 x$
$=\text { Rs. } 130 x$
$\because S . P .>C . P$,
$\therefore$ there is a gain
Gain
$=\text { Rs. } 130 x-\text { Rs. } 100 x$
$=\text { Rs. } 30 x$
Gain $\%$
$=\frac{\text { gain }}{\text { C.P. }} \times 100$
$=\frac{30 x}{100 x} \times 100$
$=30 \%$
View full question & answer→Question 195 Marks
A trader fixes the selling price of his goods at $50\%$ above the cost price. He sells half of his stock at this price, a quarter of his stock at a discount of $20\%$ on the original selling price, and the rest at a discount of $36\%$ on the original selling price. Find the gain percent altogether.
AnswerLet the $C.P.$ of each article bought $= Rs. 100$
Let the number of articles bought $=x$
$\therefore C . P$, of the articles $=R s .100 x$
$M.P.$ of the articles
$=\text { Rs. } 100+50 \%$ of $\text { Rs. } 100$
$=\text { Rs. } 150$
Stage $1:$
No. of articles sold at $Rs. 150=\frac{x}{2}$
$\therefore S.P.$ of $\frac{x}{2}$ articles
$=\operatorname{Rs} .\left(150 \times \frac{x}{2}\right)$
$= Rs .75 x$
Stage$ 2 :$
Discount
$=20 \%$ of $\text {Rs. } 150$
$=\frac{20}{100} \times \text { Rs. } 150$
$=\text { Rs. } 30$
$\therefore \text { S.P. }$
$=\text { Rs. } 150-\text { Rs. } 30$
$=\text { Rs. } 120$
No. of articles sold at $Rs. 120=\frac{x}{4}$
$\therefore S.P.$ of $\frac{x}{2}$ articles
$=Rs. \left(120 \times \frac{x}{4}\right)$
$= Rs .30 x$
Stage $3 :$
Discount
$=36 \%$ of $\text {Rs. } 150$
$=\frac{36}{100} \times \text { Rs. } 150$
$=\text { Rs. } 54$
No. of articles sold at $Rs. 96=\frac{x}{4}$
$\therefore S.P .$ of $\frac{x}{2}$ articles
$=Rs.\left(96 \times \frac{x}{4}\right)$
$= Rs .24 x$
Total $S.P.$ of all articles
$=\text { Rs. } 75 x+\text { Rs. } 30 x+R s .24 x$
$=\text { Rs. } 129 x$
$\because S . P .>C . P r_1$
$\therefore$ there is a gain
Gain
$=\text { Rs. } 129 x-R s .100 x$
$=R s, 29 x$
$=\text { Rs. } 129 x-\text { Rs. } 100 x$
$=\text { Rs, } 29 x$
Gain $\%$
$=\frac{\text { gain }}{\text { C.P. }} \times 100$
$=\frac{29 x}{100 x} \times 100$
$=29 \% .$
View full question & answer→Question 205 Marks
The list price of a watch is $Rs.4000.$ It is available either at $25\%$ flat discount or at successive discounts of $15\%$ and $12\%. $ Calculate the better offer and the amount paid in the second offer.
AnswerSuccessive discounts of $15 \%$ and $12 \%$ is equivalent to
$\left(1-\frac{15}{100}\right)\left(1-\frac{12}{100}\right) $
$=1-\frac{85}{100} \cdot \frac{88}{100} $
$=1-\frac{7480}{10000} $
$=0.2520 $
$=25.2 \%$
So, against a flat discount of $25 \%$, two successive discounts of $15 \%$ and $12 \%$ is better.
$\therefore$ Discount in the second
$=25.2 \%$ of $\text {Rs. } 4000 $
$=\frac{25.2}{100} \times 4000 $
$=\text { Rs. } 1008$
$\therefore$ Amount paid in the second
$=\text { M.P. }-$ Discount
$=\text { Rs. } 4000-\text { Rs. } 1008 $
$=\text { Rs. } 2992 .$
View full question & answer→Question 215 Marks
The marked price of a shirt is $Rs.800.$ Find the selling price, if he allows successive discounts of $15\%, 10\%$ and $8\%.$
AnswerGiven, $M.P.$ of the shirt $= Rs. 100$
First discount $=15 \%$
$\frac{\text { S.P. } 1}{M_{. P}}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\dot{S}_{.}}{800}=1-\frac{15}{100} $
$\Rightarrow \text { S.P. }{ }_1=\frac{85}{100} \times \text { Rs. } 800 $
$=\text { Rs. } 680$
Second discount $=10 \%$
$\frac{\text { S.P. } 2}{\text { S.P }}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\text { S.P. } 2}{680}=1-\frac{10}{100} $
$\Rightarrow \text { S.P. } ._2=\frac{90}{100} \times \text { Rs. } 680 $
$=\text { Rs. } 612 $
Third discount $=8 \%$
$\frac{\text { S.P. } 3}{\text { S.P. }_2}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{S_3}{612}=1-\frac{8}{100} $
$\Rightarrow \text { S.P.3 }=\frac{92}{100} \times \text { Rs. } 612 $
$=\text { Rs. } 563.04$
$\therefore$ Selling Price of the shirt $= Rs.563.04.$
View full question & answer→Question 225 Marks
A shopkeeper allows two successive discounts of $10\%$ and $15\%$ on his articles. If he gets $Rs.2295$ for an article, find its marked price.
AnswerLet the marked price be $Rs. 100$
First discount $=10 \% $
$\frac{\text { S.P. } 1}{\text { M.P.P. }}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\text { S.P. } 1}{x}=1-\frac{10}{100} $
$\Rightarrow \text { S.P. } \cdot \frac{90}{100} x $
$=\text { Rs.0.9x }$
Second discount $=15 \%$
$\frac{\text { S.P.2 }}{M_{\cdot} \cdot P_1}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{S_{\cdot 2}}{0.9 x}=1-\frac{15}{100} $
$\Rightarrow \text { S.P. }{ }_1=\text { Rs. } \frac{85}{100} \times 0.9 x $
$=\text { Rs. } 0.765 x $
$\text { ATQ. } $
$0.765 x=2295 $
$\therefore x=3000$
$\therefore$ The marked price is $Rs. 3000 .$
View full question & answer→Question 235 Marks
Find the single discount which is equivalent to successive discounts of $20\%, 10\%$ and $5\%$. Hence find the selling price of an article marked at $Rs.2500.$
AnswerLet the marked price be $Rs. 100$
First discount$=20 \%$
$\frac{\text { S.P. } 1}{\text { M.P. }}=1-\frac{\text { discount }}{100}$
$\Rightarrow \frac{S . P \cdot 1}{100}=1-\frac{20}{100}$
$\Rightarrow \text { S.P. } \cdot 1$
$=\text { Rs. } 80$
Second discount $=10 \%$
$\frac{\text { S.P.2 }}{\text { S.P.P }}=1-\frac{\text { discount }}{100}$
$\Rightarrow \frac{\text { S.P.2 }}{80}=1-\frac{10}{100}$
$\Rightarrow \text { S.P. }{ }_2=\frac{90}{100} \times \text { Rs. } 80$
$=\text { Rs. } 72$
Third discount $=5 \%$
$\frac{\text { S.P. } 3}{\text { S.P }_2}=1-\frac{\text { discount }}{100}$
$\Rightarrow \frac{\text { S.P.3 }}{72}=1-\frac{5}{100}$
$\Rightarrow S.P. 3=\frac{95}{100} \times Rs. 72$
$=Rs. 68.4$
$\therefore$ Net discount
$= M.P. - S.P. 3$
$=Rs.(100-68.4)$
$=Rs. 31.6$
$\therefore$ Discount $\%=31.6 \%$
$\frac{\text { S.P. }}{\text { M.P. }}=1-\frac{\text { discount }}{100}$
$\Rightarrow \frac{\text { S.P. }}{2500}=1-\frac{31.6}{100}$
$\Rightarrow S.P. =\frac{68.4}{100} \times Rs. 2500$
$= Rs .1710$.
View full question & answer→Question 245 Marks
Find the single discount which is equivalent to successive discounts of $10\%, 8\%$ and $5\%.$
AnswerLet the marked price be $Rs. 100$
First discount$=10 \% $
$\frac{\text { S.P. } 1}{M \cdot P_1}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\text { S.P. } 1}{100}=1-\frac{10}{100} $
$\Rightarrow \text { S.P. } \cdot \frac{90}{100} \times \text { Rs. } 100 $
$=\text { Rs. } 90$
Second discount $=8 \%$
$\frac{\text { S.P.2 }}{\text { S.P. } 1_1}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\text { S.P.2 }_2}{90}=1-\frac{8}{100} $
$\Rightarrow \text { S.P. } 2=\frac{92}{100} \times \text { Rs. } 90 $
$=\text { Rs. } 82.8$
Third discount $=5 \%$
$\frac{\text { S.P.3 }}{\text { S.P } P_2}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\text { S.P.3 }_3}{82.8}=1-\frac{5}{100} $
$\Rightarrow \text { S.P.3 }=\frac{95}{100} \times \text { Rs. } 82.8 $
$=\text { Rs.78.66 }$
$\therefore$ Net discount
$=\text { M.P. }- \text { S.P.3 } $
$=\text { Rs. }(100-78.66) $
$=\text { Rs. } 21.34$
$\therefore$ Discount $\%=21.34 \%$.
View full question & answer→Question 255 Marks
Find the single discount which is equivalent to successive discount of $20\%, 15\%$ and $10\%.$
AnswerLet the marked price be $Rs. 100$
First discount $=20 \%$
$\frac{S . P \cdot 1}{M \cdot P_{\cdot}}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\text { S.P. } 1}{100}=1-\frac{20}{100} $
$\Rightarrow \text { S.P. } 1=\frac{80}{100} \times \text { Rs. } 100 $
$=\text { Rs. } 80$
Second discount $=15 \%$
$\frac{\text { S.P. } 2^2}{\text { S.P } P_1}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\text { S.P.2 }}{80}=1-\frac{15}{100} $
$\Rightarrow \text { S.P. }_{\cdot 2}=\frac{85}{100} \times \text { Rs. } 80 $
$=\text { Rs. } 68$
Third discount $=10 \%$
$\frac{\text { S.P.3 }}{S_2 \cdot P_2}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{ S . P_3}{68}=1-\frac{10}{100} $
$\Rightarrow \text { S.P.3 }=\frac{90}{100} \times \text { Rs. } 68 $
$=\text { Rs. } 61.2$
$\therefore$ Net discount
$=\text { M.P. }- \text { S.P.3 } $
$=\text { Rs. }(100-61.2) $
$=\text { Rs.38.8 }$
$\therefore$ Discount $\%=38.8 \%$.
View full question & answer→Question 265 Marks
A dealer is selling an article marked $Rs.2000$ at a discount of $20\%.$ Find the selling price and the cost price of if he makes a profit of $25\%.$
AnswerGiven, $M.P.$ of an article $=R s .2000$
Discount$=20 \% $
$\frac{\text { S.P. }}{\text { M.P. }}=1-\frac{\text { discount }}{100} $
$\Rightarrow \frac{\text { S.P. }}{2000}=1-\frac{20}{100} $
$\Rightarrow \text { S.P. }=\frac{80}{100} \times \text { Rs. } 2000 $
$=\text { Rs. } 1600 $
$\therefore$ Selling price of the article$=\text { Rs. } 1600 $
Now. gain$=25 \% $
$\frac{\text { S.P. }}{\text { C.P.P }}=1+\frac{\text { gain }}{100} $
$\Rightarrow \frac{1600}{\text { C.P. }}=1+\frac{25}{100} $
$\Rightarrow \text { C.P. }=1600 \times \frac{100}{125} $
$=\text { Rs. } 1280 .$
View full question & answer→Question 275 Marks
A shopkeeper allows a discount of $12.5\%$ on the marked price and makes a profit of $20\%.$ If the cost price is $Rs. 4200,$ what should be the marked price?
Answer$C.P. = Rs. 4200,$ discount $=12.5 \%$, profit $\%=20 \%$
profit $\%=\frac{\text { profit }}{\text { C.P. }} \times 100$
$\Rightarrow 20=\frac{\text { profit }}{4200} \times 100 $
$\Rightarrow$ profit $=\frac{20 \times 4200}{100} $
$\Rightarrow$ profit $=\text { Rs. } 840 $
$\text { S.P. }=\text { Rs. } 4200+\text { Rs. } 840 $
$=\text { Rs. } 5040 $
$\text { S.P. }=\left(1-\frac{d}{100}\right)$ of $\text {M.P. } $
$\Rightarrow 5040=\left(1-\frac{12.5}{100}\right) \times \text { M.P. } $
$\Rightarrow 5040=\frac{87.5}{100} \times \text { M.P. } $
$\Rightarrow \frac{5040 \times 100}{87.5}=\text { M.P. } $
$\Rightarrow \text { M.P. }=\text { Rs. } 5760$
Hence, the price he should mark the article at is $Rs. 5760$
View full question & answer→Question 285 Marks
A dealer is selling an article marked $Rs. 8000$ at a discount of $15\%.$ Find the selling price of the article and the cost price if the marked price is $25\%$ above the cost price.
Answer$\text { M.P. }=\text { Rs. } 8000,$ discount $=15 \% $
$\text { S.P. }=\left(1-\frac{d}{100}\right)$ of $\text {M.P. } $
$\Rightarrow \text { S.P. }=\left(1-\frac{15}{100}\right) \times 8000 $
$\Rightarrow \text { S.P. }=\frac{85}{100} \times 8000 $
$\Rightarrow \text { S.P. }=\text { Rs. } 6800$
Let the cost price be $Rs. x$
Given that the $M.P.$
$=x+25 \%$ above the $C.P.$
$\Rightarrow 8000=x+25 \%$ of $C.P.$
$\Rightarrow 8000= x +\frac{25}{100} \times x$
$\Rightarrow 8000= x +\frac{x}{4}$
$\Rightarrow 8000=\frac{5 x}{4}$
$\Rightarrow x =\frac{8000^2 \times 4}{5}$
$\Rightarrow x = Rs .6400$
So, the $C.P.$ is $Rs. 6400 .$
Hence, the $S.P.$ of the article is $Rs. 6800$ and the $C.P.$ is $Rs. 6400 .$
View full question & answer→Question 295 Marks
A shopkeeper allows $20\%$ discount on his article. What price must he mark on an article, which costs him $Rs.1750,$ to make a profit of $20\%?$
Answer$C.P. =Rs. 1750,$ discount $=20 \%$, profit $\%=20 \%$
profit $\%=\frac{\text { profit }}{\text { C.P. }} \times 100$
$\Rightarrow 20=\frac{\text { profit }}{1750} \times 100 $
$\Rightarrow$ profit $=\frac{20 \times 1750}{100} $
$\Rightarrow$ profit $=\text { Rs. } 350 $
$\text { S.P. }=\text { Rs. } 1750+\text { Rs. } 350 $
$=\text { Rs. } 2100 $
$\text { S.P. }=\left(1-\frac{d}{100}\right) \text { of M.P. } $
$\Rightarrow 2100=\frac{80}{100} \times \text { M.P. } $
$\Rightarrow \frac{2100 \times 100}{80}=\text { M.P. } $
$\Rightarrow \text { M.P. }=\text { Rs. } 2625$
Hence, the price he should mark the article at is $Rs. 2625 .$
View full question & answer→Question 305 Marks
A tradesman sells his goods at $10\%$ discount. What Price should he mark on an article that costs him $Rs. 2400$, to gain $12.5\%$?
Answer$C.P. = Rs. 2400$, discount $=10 \%$, profit $\%=12.5 \%$
profit $\%=\frac{\text { profit }}{\text { C.P. }} \times 100$
$\Rightarrow 12.5=\frac{\text { profit }}{2400} \times 100$
$\Rightarrow$ profit $=\frac{12.5 \times 2400}{100}$
$\Rightarrow$ profit $=Rs .300$
$S.P. =Rs.2400+R s .300$
$=Rs. 2700$
$S.P. =\left(1-\frac{d}{100}\right)$ of $M.P.$
$\Rightarrow 2700=\left(1-\frac{10}{100}\right) \times M . P$.
$\Rightarrow 2700=\frac{9}{100} \times M . P$.
$\Rightarrow \frac{2700 \times 100}{90}=$ M.P.
$\Rightarrow M.P. = Rs. 3000$
Hence, the price he should mark the article at is $Rs. 3000 .$
View full question & answer→Question 315 Marks
The cost of production of a video game is $Rs.5200.$ This is divided between material, labour and overheads in the ratio $5:6:2.$ If the video game is marked at a price that gives a $30\%$ profit, find the marked price. If the cost of material, labour and overheads increased by $40\%, 30\%$ and $10\%$ respectively, calculate the cost of manufacturing the video game now and the marked price so as to get the same percentage as before.
AnswerTotal cost of production $= Rs. 5200$
The ratio of material: labour: overhead $=5: 6: 2$
$\therefore$ Total of the ratio
$=5+6+2$
$=13$
$\therefore$ Cost of material
$=\operatorname{Rs} .\left(\frac{5}{13} \times 5200\right)$
$=\text { Rs. } 2000$
$\therefore$ Cost of labor
$=\operatorname{Rs} \cdot\left(\frac{6}{13} \times 5200\right) $
$=\text { Rs. } 2400$
$\therefore$ Cost of overhead
$=\text { Rs. }\left(\frac{2}{13} \times 5200\right) $
$=\text { Rs. } 800$
Cost price of the video game $= Rs. 55200$
Profit $=30 \% $
$\therefore$ Profit
$=30 \%$ of $\text {Rs. } 5200 $
$=\text { Rs. } 1560 $
$\therefore \text { S.P. } $
$=\text { Rs. } 5200+\text { Rs. } 1560 $
$=\text { Rs. } 6760$
So, marked price is $Rs. 6760$
Cost of material $= Rs. 2000$
Increase $=40 \%$
$\therefore$ Increase
$=40 \%$ of $Rs. 2000$
$=\text { Rs } 800$
$\therefore$ New cost of material
$=\text { Rs. } 2000+R s .800$
$=\operatorname{Rs} 2800$
Cost of labour $= Rs. 2400$
Increase $=30 \%$
$\therefore$ Increase
$=30 \%$ of $\text {Rs. } 2400$
$=\text { Rs. } 720$
$\therefore$ New cost of labour
$=\text { Rs. } 2400+R s .720$
$=\text { Rs. } 3120$
Cost of overheads $= Rs. 800$
Increase $=10 \%$
$\therefore$ Increase
$=10 \%$ of $\text {Rs } 800 $
$=\text { Rs. } 80 $
$\therefore$ New cost of overheads
$=R s .800+R s .80 $
$=\text { Rs. } 880 $
$\therefore$ Cost of manufacturing now
$=\operatorname{Rs} .(2800+3120+880) $
$=\text { Rs. } 6800 $
Profit $=30 \% $
$\frac{\text { S.P. }}{\text { C.P. }}=1+\frac{\text { Profit }}{100} $
$\Rightarrow \frac{\text { S.P. }}{6800}=1+\frac{30}{100} $
$\Rightarrow \frac{\text { S.P. }}{6800}=\frac{100+30}{100} $
$\Rightarrow \text { S.P. }=\frac{130}{100} \times 6800 $
$=\text { Rs. } 8840 $
The cost of manufacturing the video game now is $Rs. 6800 ,$
And the marked price now is $Rs.8840.$
View full question & answer→Question 325 Marks
A firm dealing in computers, allows $5\%$ discount on the marked price of each system. What price must be marked on a computer set which costs $Rs. 20,000$ to assemble, so as to make a profit of $25\%?$
AnswerLet the marked price be $Rs. x$
$C.P.$ of the computer set $=\text { Rs. } 20000$
Profit $\%$
$=\frac{\text { profit }}{\text { C.P. }} \times 100$
$\Rightarrow 25=\frac{\text { profit }}{20000} \times 100$
$\Rightarrow$ profit $=\text { Rs. } 5000$
So, $\text {S.P. }$
$=\text { C.P. }+$ Profit
$=\text { Rs. } 20000+\text { Rs. } 5000$
$=\text { Rs. } 25000 $
Given that a discount of $5 \%$ is given on the $M.P.$
So, $S.P.$
$=\text { Rs. } x-5 \%$ of the $\text {M.P. }$
$ \Rightarrow \text { Rs. } 25000=x-\frac{5}{100} \times x$
$\Rightarrow \text { Rs. } 25000=\frac{95 x}{100}$
$\Rightarrow x = Rs. 26315.7$9 approx
Hence, the price that should be marked is approximately $Rs.26315.79.$
View full question & answer→Question 335 Marks
An article costs $Rs. 2000$ to a manufacturer who lists its price at $Rs. 2500.$ He sells it to a trader at a discount of $5\%.$ The trader gets a further discount of $5\%$ for cash payment. Find the amount that the trader pays to the manufacturer and the profit percent that the manufacturer makes on the sale.
AnswerList price of the article $= Rs. 2500$
$C.P.$ of the article $= Rs. 2000$
$S.P.$ of the article at $5 \%$ discount
$=Rs. 2500-5 \%$ of $Rs. 2500$
$=Rs.2500-\frac{5}{100} \times Rs. 2500$
$= Rs. 2375$
Since trader gets a $5 \%$ additional discount for cash payment,
so, amount paid by the trader
$=\text { Rs. } 2375-5 \%$ of $\text {Rs. } 2375 $
$=\text { Rs. } 2375-\frac{5}{100} \times \text { Rs. } 2375 $
$=\text { Rs. } 2375-\text { Rs. } 118.75 $
$=\text { Rs. } 2256.25$
Profit made by the manufacturer
$=$List price $- \text { S.P. } $
$=\text { Rs. } 2500-\text { Rs. } 2256.25 $
$=\text { Rs. } 243.75$
So, profit $\%$
$=\frac{\text { profit }}{\text { C.P. }} \times 100$
$=\frac{243.75}{2000} \times 100 $
$=12.18 \%$
Hence, the amount that the trader pays is $Rs. 2256.25$ and the profit% that the manufacturer makes on the sale is $12.18 \%$.
View full question & answer→Question 345 Marks
Gurmeet sells an article priced at $Rs. 25,000$. He gives a discount of $8\%$ on the first $Rs. 20,000$ and $5\%$ on the remaining amount. Manjeet also sells another article of the same kind priced at $Rs. 25,000$. He gives a discount of $6\%$ on the total price. Calculate the actual price charged by Gurmeet and Manjeet for the articles.
AnswerGurmeet gives a discount of $8 \%$ on the first $Rs. 20000$
So, $S.P.$ on $Rs. 20000$
$=\text { Rs. } 20000-\frac{8}{100} \text { (Rs. 20000) }$
$=\text { Rs. } 20000-\text { Rs. } 1600$
$=\text { Rs. } 18400$
So, $S.P.$ on $Rs. 20000$
Gurmeet give a discount of $5 \%$ on the first $Rs. 5000$
$=\text { Rs. } 5000-\frac{5}{100}(\text { Rs. 5000) }$
$=\text { Rs. } 5000-\text { Rs. } 250$
$=\text { Rs. } 4750$
So, actual price at which Gurmeet sells the article
$=\text { Rs. } 18400+\text { Rs. } 4750$
$=\text { Rs. } 23150$
Manjeet gives a discount of $6 \%$ on the first $Rs. 25000$
So, $S.P.$ on $Rs. 25000$
$=\text { Rs. } 25000-\frac{6}{100} \text { (Rs.25000) }$
$=\text { Rs. } 25000-\text { Rs. } 1500$
$=\text { Rs. } 23500$
So, actual price at which Manjeet sells the article is $Rs.23150$, and that at which Gurmeet sells the article is $Rs. 23150.$
View full question & answer→Question 355 Marks
The catalogue price of a laptop is $Rs.43200.$ If it is sold at a discount of $16\%$ of the catalogue price, a gain of $26\%$ is made. Find the gain or loss per cent if it is sold for $Rs.9000$ below the catalogue price.
AnswerGiven that the catalogue price of the laptop $= Rs. 43200$
$S.P.$ after the discount
$=\text { Rs. } 43200-\text { Rs. } \frac{16}{100} \times 43200 $
$=\text { Rs. } 43200-\text { Rs. } 6912 $
$=\text { Rs. } 36288 $
$\text { C.P. }=\text { S.P .} -$ Profit
$=\text { Rs. } 36288 -$ Profit
So, Profit $\%$
$=\frac{\text { profit }}{\text { C.P. }} \times 100$
$\Rightarrow 26=\frac{\text { profit }}{36288-\text { profit }} \times 100$
$\Rightarrow 26(36288$ - Profit $)=$ profit $\times 100$
$\Rightarrow 943488-26$ profit $=100$ profit
$\Rightarrow 94388=126$ profit
$\Rightarrow$ profit $=\frac{943488}{126}$
$\Rightarrow$ profit $= Rs. 7488$
So, $C.P. = Rs. 36288 - Rs. 7488$
$=R s .28800$
If $S.P. = Rs. 43200 - Rs. 9000$
$= Rs. 34200$
Since, $S.P. > C.Pr$,
so again was made
$=\text { Rs. } 34200-R s .28800$
$=\text { Rs. } 5400$
Profit $\%$
$=\frac{5400}{28800} \times 100 $
$=18.75 \%$
Hence, the gainpercent would be $18.75 \%$.
View full question & answer→Question 365 Marks
A publisher gives his distributor a discount of $30\%$ on the printed price of the books. The distributor sells those books to a bookseller at $23\%$ discount on the printed price and the bookseller sells these books at their printed price. Find the profit percent made by the distributor and the bookseller.
AnswerLet the printed price of the books be $Rs.x$
Discount given by the publisher
$ =30 \%$ of $\text {Rs.x }$
$=\frac{30}{100} \times \text { Rs. } x$
$=\text { Rs. } \frac{30 x}{100} $
So, the distributor bought the books at $Rs. x-Rs. \frac{30 x}{100}$
$=\operatorname{Rs} \cdot \frac{70 x}{100}$
Discount given by the distributor
$ =\text { Rs. } 23 \%$ of $\text {Rs.x }$
$=\text { Rs. } \frac{23}{100}$ of $\text {Rs. } x$
$=R s \cdot \frac{23 x}{100} $
So, the bookseller purchased the books at $Rs. x - Rs. \frac{23 x}{100}$
$= Rs \cdot \frac{77 x}{100}$
Profit made by the distributor
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. } \frac{77 x}{100}-\text { Rs. } \frac{70 x}{100}$
$=\text { Rs. } \frac{7 x}{100}$
Profit $\%$
$ =\frac{\text { profit }}{\text { C.P. }} \times 100$
$=\frac{\frac{7 x}{100}}{\frac{70 x}{100}} \times 100$
$=10 \%$
$S.P.$ at which the bookseller sold the books $= Rs.x$
So, profit
$=\text { S.P. }- \text { C.P. }$
$= Rs. x-R s, \frac{77 x}{100}$
$=\text { Rs. } \frac{53 x}{100}$
Profit $\%$
$ =\frac{\text { profit }}{\text { C.P. }} \times 100$
$=\frac{\frac{23 x}{100}}{\frac{77 x}{100}} \times 100$
$=29 \frac{67}{77} \% $
Hence, the profit $\%$ made by the distributor is $10 \%$ and that made by the bookseller is $29 \frac{67}{77} \%$.
View full question & answer→Question 375 Marks
A dealer marks his goods $25\%$ above the cost price and then allows $10\%$ discount on it. What is the cost price of an article on which he gains $Rs. 575$?
AnswerLet the $C.P.$ be $Rs. 100 ,$
So, $M.P. =C.P. +25 \%$ of $C.P.$
$=100+\left(\frac{25}{100} \times 100\right)$
$=\text { Rs. } 125$
Discount
$=10 \%$ on $\text {M.P. }$
$=\frac{10}{100} \times 125$
$=\text { Rs. } 125$
So, $S.P.$ of the goods
$=\text { M.P. }-$ Discount
$=\text { Rs. } 125-\text { Rs. } 12.5$
$=\text { Rs. } 112.5$
Profit
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. } 112.5-R_s .100$
$=\text { Rs. } 12.5$
When the $S.P.$ is $Rs. 112.5$ , the profit is $Rs. 12.5$
So, when the gain is $Rs.960,$
the $S.P.$
$=\frac{112.5 \times 575}{12.5}$
$=\text { Rs. } 5175$
$\text { C.P. }=\text { S.P.} -$ Profit
$=\text { Rs. } 5175-\text { Rs. } 575$
$=\text { Rs. } 4600$
Hence, the cost price of and article on which he gains$ Rs. 575$ is $Rs. 4600 .$
View full question & answer→Question 385 Marks
A dealer marks his goods $45\%$ above the cost price and then allows $20\%$ discount on it. What is the cost price of an article on which he gains $Rs.960?$
AnswerLet the $C.P.$ be $Rs. 100$
So, $\text { M.P. }=\text { C.P. }+45 \%$ of $\text {C.P. }$
$=100+\left(\frac{45}{100} \times 100\right)$
$=\text { Rs. } 145$
Discount
$=20 \%$ on $\text {M.P. }$
$=\frac{20}{100} \times 145$
$=\text { Rs. } 29$
So, $\text {S.P. }$ of the goods
$=\text { M.P. }-$Discount
$=\text { Rs. } 145-\text { Rs. } 29$
$=\text { Rs. } 116$
Profit
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. } 116-\text { Rs. } 100$
$=\text { Rs. } 16 $
When the$ S.P.$ is $Rs. 116 ,$ the profit is $Rs. 16$
So, when the gain is $Rs. 960 ,$
$ \text { the S.P. }=\frac{116 \times 960}{16}$
$=\text { Rs. } 6960$
$\text { C.P. }=\text { S.P. }-$ Profit
$=\text { Rs. } 6960-\text { Rs. } 960$
$=\text { Rs. } 6000$
Hence, the cost price of and article on which he gain $Rs. 960$ is $Rs. 6000 .$
View full question & answer→Question 395 Marks
A trader allows a discount of $15\%$on the marked price of the goods in his shop. However, he still makes a gross profit of $36\%$ on the cost price. Find the profit percent, he would have made, had he sold the goods at the marked price.
AnswerLet the $C.P.$ be $Rs. 100$
Given that the profit $\%$
$=36 \%$ on the $\text {C.P. }$
Profit $\%$
$=\frac{\text { profit }}{\text { C.P. }} \times 100$
$\Rightarrow 36 \%=\frac{\text { profit }}{100} \times 100$
$\Rightarrow$ profit $=\text { Rs. } 36$
$\text { S.P. }=\text { C.P. }+ \text { Profit }$
$=100+36$
$=\text { Rs. } 136$
Let the marked price of the goods be $Rs, x.$
Discount $=15 \%$ of $M.P.$
$=\frac{15}{100} \times x$
$=\text { Rs } \frac{15 x}{100}$
So, $S.P. = M.P. -$ Discount
$\Rightarrow 136=\text { Rs. }\left(x-\frac{15 x}{100}\right)$
$\Rightarrow x =\text { Rs. } \frac{136 \times 100}{85}$
$\Rightarrow x =\text { Rs. } 160 \%$
If the goods were sold at the $M.P.$, that $S.P. = M.P.$
So, $M.P. - C.P.$
$=160-100$
$=60$
$=$ profit
Profit $\%$
$=\frac{60}{100} \times 100$
$=60 \%$
Hence, the profit percent would be $60 \%$.
View full question & answer→Question 405 Marks
A trader allows a discount of $12\%$ on the marked price of the goods in his shop. He still makes a gross profit of $21\%$ on the cost price. Find the profit percent he would have made, had he sold the goods at the marked price.
AnswerLet the $C.P.$ be $Rs. 100 .$
Given that the profit $\%=21 \%$ on the $C.P.$
Profit $\%=\frac{\text { profit }}{\text { C.P. }} \times 100$
$=21 \%=\frac{\text { profit }}{100} \times 100$
$\Rightarrow \text { profit }=\text { Rs. } 21$
$\text { S.P. }=\text { C.P. }+ \text { Profit }$
$=100+21$
$=\text { Rs. } 121$
Let the market price of the goods be $Rs. x$.
Discount $=12 \%$ of $M.P.$
$=\frac{12}{100} \times x$
$=\text { Rs. } \frac{12 x}{100}$
So, $S.P. = M.P. -$ Discount
$\Rightarrow 121=\operatorname{Rs} .\left(x-\frac{12 x}{100}\right)$
$\Rightarrow x =\text { Rs. } \frac{121 \times 100}{88}$
$\Rightarrow x =\text { Rs. } 137.5 \%$
If the goods were sold at the $M.P_{4}$ that $S.P. = M.P.$
So, $\text {M.P. }- \text { C.P. }$
$=137.7-100$
$=37.5$
$=$ profit
Profit $\%=\frac{37.5}{100} \times 100$
$=37.5 \%$
Hence, the profit percent would be $37.5 \%$.
View full question & answer→Question 415 Marks
A shopkeeper fixes the selling price of his goods at $60\%$ above the cost price. He sells half of this stock at this price, a quarter of his stock at a discount of $25\%$ on the original selling price, and the rest at a discount of $50\%$ on the original selling price. Find the gain percent altogether.
AnswerLet the cost price of each article bought $= Rs. 100 .$
Let the number of article bought $=x$
$M.P.$ of the article
$=\text { Rs. } 100+60 \%$ of $\text {Rs. } 100$
$=\text { Rs. } 100+\left(\frac{60}{100} \times 100\right)$
$=\text { Rs. } 160$
Number of articles sold at $Rs.160=\frac{x}{2}$
$\therefore \text { S.P.}$ of $\frac{x}{2}$ articles
$=\text { Rs. }\left(160 \times \frac{x}{2}\right)$
$=\text { Rs. } 80 x$
Discount
$=25 \%$ on $\text {Rs. } 160$
$=\frac{25}{100} \times 160$
$=\text { Rs. } 40$
$\therefore \text { S.P. }$
$=\text { Rs. } 160-\text { Rs. } 40$
$=\text { Rs. } 120$
Remaining number of articles scold at $Rs. 120$
$=x-\frac{x}{2}-\frac{x}{4}=\frac{x}{4}$
$\therefore S.P.$ of $\frac{x}{4}$ articles
$=\text { Rs. }\left(120 \times \frac{x}{4}\right)$
$= Rs .30 x$
Discount
$=50 \%$ on $\text { Rs. } 160$
$=\frac{50}{100} \times 160$
$=\text { Rs. } 80$
$\therefore \text { S.P. }=\text { Rs. } 160-\text { Rs. } 80$
$=\text { Rs. } 80$
Number of articles sold at $Rs. =\frac{x}{4}$
$\therefore S.P.$ of $\frac{x}{4}$ articles
$=Rs. \left(80 \times \frac{x}{4}\right)$
$= Rs .20 x$
Total $S.P.$ of all articles
$=\text { Rs. } 80 x+R s .30 x+R s .20 x$
$=130 x$
Profit
$=S \cdot P .-C \cdot P \text {. }$
$=\text { Rs. } 130 x-R s .100 x$
$=\text { Rs. } 30 x$
So,profit $\%$
$=\frac{\text { profit }}{\text { CP }} \times 100$
$=\frac{30 x}{100 x} \times 100$
$=30 \%$
Hence, the gain percent altogether is $30 \%$.
View full question & answer→Question 425 Marks
A trader fixes the selling price of his goods at $50\%$ above the cost price. He sells half of his stock at this price, a quarter of his stock at a discount of $20\%$ on the original selling price, and the rest at a discount of $36\%$ on the original selling price. Find the gain per cent altogether.
AnswerLet the cost price of each article bought $= Rs. 100 .$
Let the number of articles bought $=x$
$M.P.$ of the articles $=Rs.100+50 \%$ of $Rs. 100$
$=\text { Rs. } 100+\left(\frac{50}{100} \times 100\right)$
$=\text { Rs. } 150$
Number of articles sold at $Rs, 150=\frac{x}{2}$
$\therefore S.P.$ of $\frac{x}{2}$ articles
$=Rs. \left(150 \times \frac{x}{2}\right)$
$= Rs .75 x$
Discount $=20 \%$ on $Rs. 150$
$=\frac{20}{100} \times 150$
$= Rs .30$
$\therefore S.P.$
$= Rs. 150-Rs. 30$
$=Rs. 120$
Remaining number of articles sold at $Rs. 120$
$=x-\frac{x}{2}-\frac{x}{4}-\frac{x}{4}$
$\therefore S.P.$ of $\frac{x}{4}$ aricles
$=Rs. \left(120 \times \frac{x}{4}\right)$
$=Rs. 30 x$
Discount
$=36 \%$ on $Rs. 150$
$=\frac{36}{100} \times 150$
$=\text { Rs. } 54$
$\therefore \text { S.P. }$
$=\text { Rs. } 150-\text { Rs. } 54$
$=\text { Rs. } 96$
Number of articles sold at $Rs. =\frac{x}{4}$
$\therefore S.P.$ of $\frac{x}{4}$ articles
$=\text { Rs. }\left(96 \times \frac{x}{4}\right)$
$=\text { Rs. } 24 x$
Total $S.P.$ of all articles
$=\text { Rs. } 75 x+\text { Rs. } 30 x+R s .24 x$
$=1129 x$
Profit
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. } 129 x-\text { Rs. } 100 x$
$=\text { Rs. } 29 x$
So, profit $\%$
$=\frac{\text { Profit }}{\text { C.P. }} \times 100$
$=\frac{29 x}{100 x} \times 100$
$=29 \%$
Hence, the gainpercent altogether is $29 \%$.
View full question & answer→Question 435 Marks
The marked price of a sofa set is $Rs. 36000$ and is available in Guwahati at $ 20\%$ discount. $A$ shopkeeper from Delhi buys this article in Guwahati and spends $Rs. 1500$ on his travelling and $Rs. 1200$ on the transportation etc. of the article. Find the profit per cent made by the shopkeeper, if he sells the article in Delhi at the $a$. marked price, $b. 5\%$ discount.
Answer$M.P.$ of the sofa $= Rs. 36000$ , discount at Guwahati $=20 \%$
$\text { S.P. }=\left(1-\frac{d}{100}\right) \text { of M.P. }$
$\Rightarrow \text { S.P. }=\left(1-\frac{20}{100}\right) \times 36000$
$\Rightarrow \text { S.P. }=\frac{80}{100} \times 36000$
$\Rightarrow \text { S.P. }=\text { Rs. } 28800$
So, the $ S.P.$ at Guwahati is $Rs. 28800.$
So, total expenses
$=S.P. +$ travelling expenses $+$ transportation of the article
$=\text { Rs. } 28800+\text { Rs. } 1500+\text { Rs. } 1200$
$=\text { Rs. } 31500$
So, the $C.P.$ at Delhi $= Rs. 31500$
$a. S.P.$ at Delhi
$=$ marked price
$= Rs .36000$
So, profit
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. } 36000-\text { Rs. } 31500$
$=\text { Rs. } 4500$
Profit $\%$
$=\frac{\text { Profit }}{\text { C.P }} \times 100$
$=\frac{4500}{31500} \times 100$
$=14 \frac{2}{7} \%$
$b$. discount $=5 \%$ of $36000$
$=\frac{5}{100} \times 36000$
$=\text { Rs. } 1800$
$\Rightarrow \text { S.P. }$
$=36000-1800$
$=\text { Rs. } 34200$
So, Profit
$=S.P. - C.P.$
$=Rs. 34200-R s .31500$
$=Rs. 2700$
Profit $\%$
$=\frac{\text { Profit }}{\text { C.P }} \times 100$
$=\frac{2700}{31500} \times 100$
$=8 \frac{4}{7} \%$
View full question & answer→Question 445 Marks
Find the single discount which is equivalent to successive discounts of $20\%, 10\%$ and $5\%.$ Hence, find the selling price of an article marked at $Rs. 2500.$
AnswerLet the $M.P.$ be of the article be $Rs. x$ and a single discount be $d \ \%\ $ be equivalent to three given successive discounts of $20 \%, 10 \%$ and $5 \%$.
Equating the two selling prices of the article we get
$ \left(1-\frac{d}{100}\right)$ of $\text {Rs. x }$
$=\left(1-\frac{20}{100}\right)\left(1-\frac{10}{100}\right)\left(1-\frac{5}{100}\right)$ of $\text { Rs. x }$
$\Rightarrow\left(1-\frac{d}{100}\right) \times x=\frac{80}{100} \times \frac{90}{100} \times \frac{95}{100} \times x$
$\Rightarrow 1-\frac{d}{100}=\frac{80}{100} \times \frac{90}{100} \times \frac{95}{100}$
$\Rightarrow 1-\frac{d}{100}=\frac{684000}{1000000}$
$\Rightarrow 1-\frac{684000}{1000000}=\frac{d}{100}$
$\Rightarrow \frac{316000}{1000000}=\frac{d}{100}$
$\Rightarrow d=\frac{316000 \times 100}{1000000}$
$\Rightarrow d=3.16 \% $
$M.P.$ of the article $= Rs. 2500$
$\text { S.P. }=\left(1-\frac{31.6}{100}\right) \times 2500$
$\Rightarrow \text { S.P. }=\frac{68.4}{100} \times 2500$
$\Rightarrow \text { S.P. }=\text { Rs. } 1710$
Hence, the equivalent discount is $Rs. 31.6 \%$ and the $S.P.$ is $Rs. 1710 .$
View full question & answer→Question 455 Marks
A briefcase was sold at a profit of $10\%.$ If its cost price was $5\%$ less and it was sold for $Rs.120$ more, the gain would have been $20\%.$ Find the cost price of the briefcase.
AnswerLet the $C.P. $of briefcase be $Rs. 100$
Profit$=10 \%$
$\frac{\text { S.P. }}{\text { C.P. }}=1+\frac{\text { Profit }}{100}$
$\Rightarrow \frac{\text { S.P. }}{100}=1+\frac{10}{100}$
$\Rightarrow \frac{\text { S.P. }}{100}=\frac{100+10}{100}$
$\Rightarrow \text { S.P. }=\frac{100 \times 110}{100}$
$=\text { Rs. } 110 $
When buying at $5 \%$ less,
$C.P.$ of the briefcase
$ =\text { Rs. } 100-5 \%$ of $\text { Rs. } 100$
$=\text { Rs. }(100-5)$
$=\text { Rs. } 95$
Gain $\%=20 \%$
Gain $=\frac{20}{100} \times Rs. 95$
$=\text { Rs. } 19$
$\therefore S . P$. of the briefcase
$=Rs, 95+Rs .19$
$=\text { Rs. } 114$
$\therefore$ Difference between the two $S.P.'s$
$=\text { Rs. } 114 \text { - Rs. } 110$
$=\text { Rs. } 4$
When the difference in $S.P.$ is $Rs.4,$ the $C.P.$ of the briefcase is $Rs. 100$
$\therefore$ When the difference in $S.P.$ is $Rs. 120 ,$ the $C.P.$ of the briefcase is
$=\text { Rs. }\left(\frac{100 \times 120}{4}\right) $
$=\text { Rs. } 3000 .$
View full question & answer→Question 465 Marks
A dealer sells two refrigerators for $Rs.37500$ each. On one he makes a profit of $25\%$ while on the other he makes a loss of $25\%.$ Calculate his overall loss or profit percentage in the transaction.
AnswerFor the first refrigetator ${ }_{\text {, }}$
$\text { S.P. }=\text { Rs. } 37500$
Profit $=25 \%$
$\frac{\text { S.P. }}{\text { C.P. }}=1+\frac{\text { Profit }}{100}$
$\Rightarrow \frac{37500}{\text { C.P }}=1+\frac{25}{100}$
$\Rightarrow \frac{37500}{\text { C.P. }}=\frac{100+25}{100}$
$\Rightarrow \text { C.P. }=\frac{100}{125} \times 37500$
$=\text { Rs. } 30000$
For the second refrigerator,
$ \text { S.P. }=\text { Rs. } 37500$
Loss $=25 \%$
$\frac{\text { S.P. }}{\text { C.P. }}=1-\frac{\text { Loss }}{100}$
$\Rightarrow \frac{37500}{\text { C.P }}=1-\frac{25}{100}$
$\Rightarrow \frac{37500}{\text { C.P. }}=\frac{100-25}{100}$
$\Rightarrow \text { C.P. }=\frac{100}{75} \times 37500$
$=\text { Rs. } 50000 $
Total $C.P.$ of both the refrigerator
$=\text { Rs. } 30000+R s .50000$
$=\text { Rs. } 80000 $
Total $S.P.$ of both the refrigerator
$ =\text { Rs. } 37500 \times 2$
$=\text { Rs. } 75000$
Since $C.P. > S.P.$
so there is a loss
Loss
$=C \cdot P \cdot-S . P \text {. }$
$=\operatorname{Rs} .(80000-75000)$
$= Rs. 5000$
$1055 \%$
$ =\frac{\text { Loss }}{\text { C.P }} \times 100$
$=\frac{5000}{80000} \times 100$
$=6.25 \%$
View full question & answer→Question 475 Marks
The selling price of a computer was fixed at $Rs.32200$ so as to give a profit of $15\%.$ During a sale the price of the same computer was reduced to $Rs.29960.$ Calculate the actual profit or loss during the scale.
AnswerInitial $S..P.$ of a computer$=\text { Rs. } 3220$
Profit$=15 \%$
$\frac{\text { S.P. }}{\text { C.P. }}=1+\frac{\text { Profit }}{100}$
$\Rightarrow \frac{32000}{\text { C.P. }}=1+\frac{15}{100}$
$\Rightarrow \frac{32000}{\text { C.P. }}=\frac{100+15}{100}$
$\Rightarrow \text { C.P. }=\frac{100}{115} \times 32200$
$=\text { Rs. } 28000$
$\therefore C.P.$ of the computer $=\text { Rs. } 28000$
If the $S.P.$ of the computer is $Rs. 29960,S.P. > C.P.$
$\therefore$ There would be a profit of
$=S . P .-C . P .$
$=R s .(29960-28000)$
$=\text { Rs. } 1960 . $
View full question & answer→Question 485 Marks
The cost price of $5$ pens is the same as the selling price of $4$ of them. Find the gain percent.
AnswerLet the $S.P.$ of $4$ pens $= Rs.x$
$\therefore S . P$. of $1$ pen $= Rs. \frac{x}{4}$
$C.P.$ of $5$ pens will also be $Rs. x$
$\therefore C.P.$ of $1$ pen $= Rs. \frac{x}{5}$
As $S.P. > C.P.$
$\therefore$ Profit
$=S \cdot P .-C . P$.
$=\operatorname{Rs} .\left(\frac{x}{4}-\frac{x}{5}\right)$
$= Rs. \left(\frac{5 x-4 x}{20}\right)$
$= Rs \frac{x}{20}$
Now, Profit $\%$
$=\frac{\text { Profit }}{\text { C.P. }} \times 100$
$=\frac{\frac{x}{20}}{\frac{x}{5}} \times 100$
$=\frac{\frac{x}{5}}{20} \times \frac{5}{x} \times 100$
$=25 \%$.
View full question & answer→Question 495 Marks
By selling a cupboard for $Rs.6480,$ a merchant loses $10\%.$ Calculate his loss if he sells it for $Rs.7560.$
Answer$S.P.$ of the cupboard $= Rs. 6480$
Loss $=10 \%$
Now,
$\frac{\text { S.P. }}{\text { C.P. }}=1-\frac{\text { Loss }}{100} $
$\Rightarrow \frac{6480}{\text { C.P. }}=1-\frac{10}{100} $
$\Rightarrow \frac{6480}{\text { C.P. }}=\frac{100-10}{100} $
$\Rightarrow \text { C.P. }=\frac{100}{90} \times 6480 $
$=\text { Rs. } 7200$
Now,
$C.P.$ of the cupboard $= Rs. 7200$
$S.P.$ of the cupboard $= Rs. 7560$
$\because \text { S.P. > C.P. }$
$\therefore$ Gain
$=\text { S.P. }- \text { C.P. }$
$=\text { Rs. }(7560-7200) $
$=\text { Rs. } 360$
$\therefore$ Gain $\%$
$=\frac{\text { gain }}{\text { C.P. }} \times 100$
$=\frac{360^{\circ}}{7200} \times 100$
$=5 \%$
View full question & answer→Question 505 Marks
By selling tie for $Rs.648,$ a shopkeeper gains $8\%.$ At what price should he sell the tie to gain $10\%$?
Answer$ \text { S.P.}$ of a tie $=\text { Rs .} 648$
Gain$=8 \%$
$\frac{\text { S.P. }}{\text { C.P. }}=1+\frac{\text { Profit }}{100}$
$\Rightarrow \frac{648}{\text { C.P. }}=1+\frac{8}{100}$
$\Rightarrow \frac{648}{\text { C.P. }}=\frac{100+8}{100}$
$\Rightarrow \text { C.P. }=\frac{100}{108} \times 648$
$=\text { Rs. } 600$
Now, $C.P.$ of the tie $= Rs. 600$
Gain$=10 \%$
$\therefore$ Gain$=\frac{10}{100} \times \text { C.P. }$
$\therefore$ Gain$=\frac{10}{100} \times 600$
$=\text { Rs. } 60$
$\therefore \text { S.P. }$
$=\text { Rs. } (600+60)$
$=\text { Rs. } 660$
He must sell the tie at $Rs. 660$ to make a gain of $10 \%$.
View full question & answer→