Question 15 Marks
A dealer in Bihar supplied goods to a dealer in Mumbai. The dealer in Mumbai buys : $(i)\ 40$ articles for $800$ each at $30\%$ discount $(ii)\ 75$ articles for $1,000$ each at $20\%$ discount.If the rate of $\text{GST}$, on the whole, is $12\%$, find how much will the dealer at Mumbai pay to a dealer in Bihar.
AnswerThe dealer in Mumbai buys:
$(i) 40$ articles for $800$ each at $30 \%$ discount
Cost after Discount $=\left(800-800 \times \frac{30}{100}\right)=(800-240)=560$
Cost for $40$ articles $=40 \times 560=22400$
$(ii) 75$ articles for $1,000$ each at $20 \%$ discount.
Cost after Discount $=\left(1000-\frac{20}{100} \times 1000\right)=(1000-200)=800$
Cost for $75$ articles $=75 \times 800=60000$
Total Cost $=22400+60000=82400$
Rate of $\text {GST} =12 \%$
$\text { GST }=\left(\frac{12}{100}\right) \times 824000=9888$
dealer at Mumbai pay to dealer in Bihar $=82400+9888=Rs. 92288$
View full question & answer→Question 25 Marks
A shopkeeper in Indore sells $20$ identical articles for $₹.450$ each. Find the amount of bill if he gives a $20\%$ discount and then charges $\text{GST} = 28%$
AnswerGiven
Number of items $=20$
Price of one item $=450$
Therefore the total cost of $20$ items $=20 \times 450= Rs. 9000$
Now discount is $20 \%$
So total discount $=9000 \times \frac{20}{100}= Rs. 1800$
So discounted price $=9000-1800= Rs. 7200$
Now $\text{GST}$ on discounted price
$\text{GST} \%=28 \%$ on discounted price
So the amount of $\text{GST} =7200 \times \frac{28}{100}= Rs. 2016$
Now total bill $=$ discounted price $+$ amount of $\text{GST}$
$=7200+2016=\text { Rs. } 9216$
View full question & answer→Question 35 Marks
Some goods$/$services cost $Rs. 16,000$ and the rate of $\text{GST}$ on them is $12\%$. Find the amount of the bill, in the case of : $(i)$ intra$-$state transaction.$(ii)$ inter$-$state transaction.
AnswerCost of goods $= Rs. 16000$
Rate of $\text{GST} =12 \%$
$(i)$ Intra$-$state transaction:
$\text { SGST }=\text { CGST }=\left(\frac{12}{2}\right)=6 \%$
$ \text { CGST }=\left(\frac{6}{100}\right) \times 16000=\text { Rs. } 960$
$ \text { SGST }=\left(\frac{6}{100}\right) \times 16000=\text { Rs. } 960$
Amount of bill $=16000+960+960= Rs. 17920$
$(ii)$ Inter$-$state transaction:
Cost of goods $= Rs .16000$
$\text { IGST }=12 \%=\left(\frac{12}{100}\right) \times 16000=\text { Rs. } 1920$
Amount of bill $=16000+1920=17920$
View full question & answer→Question 45 Marks
When the rate of sale$-$tax is decreased from $9\%$ to $6\%$ for a coloured $T.V$.; Mrs. Geeta will save $Rs. 780$ in buying this $T.V$. Find the list price of the $T.V.$
AnswerLet the list price of $T.V =y$
Sales tax when the rate is $9 \%=\frac{9}{100} y$
$=>$ Sale price is $\mathrm{y}+\frac{9 \mathrm{y}}{100}$
Sales tax when the rate is $6 \%=\frac{6}{100} y$
$=>$ Sale price is $\mathrm{y}+\frac{6}{100} \mathrm{y}$
Differences of sale prices
$=y+\frac{9 y}{100}-\left(y+\frac{6 y}{100}\right)$
$ =y+\frac{9 y}{100}-y-\frac{6 y}{100}$
$ =\frac{9 y}{100}-\frac{6 y}{100}$
Saving for Geeta $=780$
Therefore we have
$780=\frac{9 y}{100}-\frac{6 y}{100}$
$ \Rightarrow \frac{3 y}{100}=780$
$\Rightarrow \mathrm{y}=\frac{780 \times 100}{3}$
$ \Rightarrow \mathrm{y}=\text { Rs. } 26000$
Thus the list price of the $T.V$ is $Rs. 26000$
View full question & answer→Question 55 Marks
The price of an article is $Rs .8,250$ which includes sales tax at $10\%$. Find how much more or less does a customer pay for the article, if the sales tax on the article : $(i)$ increases to $15\%\ (ii)$ decreases to $6\%(iii)$ increases by $2\%\ (iv)$ decreases by $3\%$
AnswerLet sale price of article $= Rs .y$
Total price inclusive of sales $\operatorname{tax}=\mathrm{Rs} .\ 8,250$
The rate of sales $\operatorname{tax}=10 \%$
According to question
$y+10 \% $ of $y=\text { Rs .} 8250$
$ \Rightarrow y+\frac{y}{10}=\text { Rs. } 8250$
$ \Rightarrow \frac{11 y}{10}=\text { Rs. } 8250$
$ \Rightarrow y=\frac{8250 \times 10}{11}=\text { Rs. } 7500$
$(i)$ New rate of sales tax $=15 \%$
New total price $= Rs. 7,500+15 \%$ of $Rs. 7,500$
$=\text { Rs. } 7500+\frac{15}{100} \times 7500$
$ =\text { Rs. } 7500+\text { Rs. } 1125=\text { Rs. } 8625$
More money paid $= Rs. 8,625- Rs. 8,250= Rs. 375 \ (ii)$ New rate of sales tax $=6 \%$ New total price $= Rs. 7,500+6 \%$ of $Rs. 7,500$
$=\text { Rs. } 7500+\frac{6}{100} \times 7500$
$ =\text { Rs. } 7500+\text { Rs. } 450=\text { Rs. } 7950$
Less money paid $= Rs. 8,250 - Rs. 7,950= Rs. 300$
$(iii)$ New rate of sales tax $=(10+2) \%=12 \%$
New total price $= Rs. 7,500+12 \%$ of $Rs. 7,500$
$= Rs. 7500+\frac{12}{100} \times 7500$
$= Rs. 7500+ Rs. 900= Rs. 8400$
More money paid $= Rs. 8,400- Rs. 8,250= Rs. 150$
$(iv)$ New rate of sales tax $=(10-3) \%=7 \%$
New total price $= Rs. 7,500+7 \%$ of $Rs. 7,500$
$= Rs. 7500+\frac{7}{100} \times 7500$
$= Rs. 7500 + Rs. 525 = Rs. 8025$
Less money paid $= Rs. 8,250- Rs. 8,025= Rs. 225$
View full question & answer→Question 65 Marks
The price of a $T.V.$ set inclusive of sales tax of $9\%$ is $Rs .13,407$. Find its marked price. If sales tax is increased to $13\%$, how much more does the customer has to pay for the $T.V$.?
AnswerTotal price paid for $T.V. = Rs .13,407$
The rate of sales $\operatorname{tax}=9 \%$
Let sale price $= Rs .y$
According to question
$y+9 \% $ of $ y= Rs .13407$
$ \Rightarrow y+\frac{9 y}{100}=Rs. 13407$
$ \Rightarrow \frac{109 y}{100}=Rs. 13407$
$ \Rightarrow y=\frac{13407 \times 100}{109}=Rs. 12300$
New rate of sales $\operatorname{tax}=13 \%$
New total price for $T.V. = Rs. 12,300+13 \%$ of $Rs. 12,300$
$= Rs. 12300+\frac{13}{100} \times 12300$
$ = Rs. 12300+Rs. 1599$
$=Rs. 13899$
More money paid $= Rs. 13,899 - Rs. 13,407= Rs. 492$
View full question & answer→Question 75 Marks
Sarita purchases biscuits costing $Rs .158$ on which the rate of sales tax is $6\%$. She also purchases some cosmetic goods costing $Rs.354$ on which the rate of sales tax is $9\%$. Find the total amount to be paid by Sarita.
AnswerSale price of biscuits $= Rs .158$
Rate of sales tax on biscuits $=6 \%$
Amount paid for biscuits $= Rs .158+6 \%$ of $Rs .158$
$=Rs. 158+\frac{6}{100} \times 158$
$ =Rs.158+Rs.9.48$
$ =Rs.167.48$
The sale price of cosmetic goods $= Rs. 354$
Rate of sales $\operatorname{tax}=9 \%$
Amount paid for cosmetic goods $= Rs .354+9 \%$ of $Rs. 354$
$=Rs. 354+\frac{9}{100} \times 354$
$ = Rs. 354+Rs .31.86$
$ =Rs. 385.86$
Total amount paid by Sarita $= Rs. 167.48 + Rs. 385.86$
$=Rs. 553.34$
View full question & answer→Question 85 Marks
A shopkeeper marks his goods at $30$ percent above the cost price and then gives a discount of $10$ percent. Find his gain percent.
AnswerLet $\text{C.P}.$ of the goods $= Rs. 100$
$\text{M.P}$. of the goods $= Rs. 100+ Rs. 30$
$= Rs. 130$
Discount $=\frac{10}{100} \times Rs. 130$
$=Rs. \frac{1300}{100}$
$= Rs. 13$
$\text{S.P}$. of the goods $=\text{ M.P}. -$ Discount
$= Rs. 130-Rs. 13$
$= Rs. 117$
Gain $=\text{S.P. - C.P}.$
$= Rs. 117 - Rs. 100$
$= Rs. 17$
Gain $\%=\frac{\text { Gain }}{\text { C.P. }} \times 100$
$=\frac{17}{100} \times 100$
$=17 \%$
View full question & answer→Question 95 Marks
A shop$-$keeper buys an article for $Rs.450.$ He marks it at $20%$ above the cost price. Find : $(i)$ the marked price of the article. $(ii)$ the selling price, if he sells the articles at $10$ percent discount. $(iii)$ the percentage discount given by him, if he sells the article for $Rs.496.80$
Answer$\text{C.P}$. of the article $= Rs. 450$
$(i)$ The marked price of the article
$=\frac{100+20}{100} \times Rs. 450$
$ = Rs. \frac{120}{100} \times 450=12 \times 45=Rs. 540$
$\therefore$ Marked price of the article $= Rs. 540$
$(ii)$ Discount $=\frac{10}{100} \times \text{M.P}.$
$=\frac{10}{100} \times Rs. 540$
$ = Rs. 54$
$\text{S.P. = M.P.} - $Discount
$= Rs. 540-Rs. 54$
$= Rs. 486$
$(iii) \text{S.P.} = Rs. 496.80$
$\text { M.P. }=Rs. 540$
Discount $=\text{M.P. - S.P}.$
$= Rs. 540 - Rs. 496.80$
$=Rs. 43 \cdot 20$
Discount $\%=\frac{\text { Discount }}{\text { M.P. }} \times 100$
$ =\frac{43.20}{540} \times 100$
$ =\frac{4320}{540} \%$
$ =8 \%$
View full question & answer→Question 105 Marks
Thirty articles are bought at $Rs. 450$ each. If one$-$third of these articles be sold at a $6\%$ loss; at what price must each of the remaining articles be sold in order to make a profit of $10\%$ on the whole?
Answer$\text{C.P}$. of one article $= ₹.450$
$\text{C.P}$. of $30$ articles $= ₹.450 \times 30 = ₹.13500$
$\text{C.P}$. of $\frac{1}{3}$ articles $=\text {₹} 450\times \frac{30}{3}$
$= ₹4500$
Loss of $= 6\%$
$\therefore \text{S.P}$. of $10$ articles = $\frac{\text { C.P. } \times(100-\text { Loss } \%)}{100}$
$=\text {₹}\frac{4500 \times(100-6)}{100}$
$=\text {₹}\frac{4500 \times 94}{100}$
$= ₹.4230$
$\text{C.P}$. of remaining articles $= ₹.4500 \times 20$
$= ₹.90000$
Profit on the whole $= 10\%$
$\therefore$ Total $\text{S.P}.$ of $30$ articles
$=₹.\frac{13500 \times(100+10)}{100}$
$=₹.\frac{13500 \times 110}{100}$
$= ₹.14850$
$\therefore \text{S.P}.$ of the remaining $20$ articles.
$= ₹.14850 − ₹.4230 = ₹.10620$
$\therefore \text{S.P}$. of $1$ article $=₹.\frac{10620}{20}=₹.531$
View full question & answer→Question 115 Marks
A ready$-$made garments shop in Delhi, allows a $20$ percent discount on its garments and still makes a profit of $20$ percent. Find the marked price of a dress which is bought by the shop$-$keeper for $Rs.400.$
Answer$\text{C.P}$. of the dress $= Rs.400$
Profit $=\frac{20}{100} \times Rs. 400= Rs. 80$
$\text{S.P. = C.P}. +$ Profit
$= Rs.400 + Rs.80$
$= Rs.480$
Let, $\text{M.P}$. of the dress $= Rs.100$
Discount $@ 20\% =\frac{20}{100} \times Rs.100= Rs. 20$
$\text{S.P}$. of the dress $= \text{M.P}. −$ Discount
$= Rs.100 − Rs.20$
$= Rs.80$
If $\text{S.P.}$ of the dress is $₹.80$; then $\text{M.P}. =\text {₹} 100$
If $\text{S.P}$. of the dress is $₹.1$ then $\text{M.P.} =₹\frac{100}{80}$
If $\text{S.P}.$ of the dress is $₹.480$ then $\text{M.P}.$
$=₹\frac{100}{80}\times 480$
$= ₹100 \times 6 = 600$
$\therefore \text{M.P}$. of the dress $= ₹600$
View full question & answer→Question 125 Marks
Mohan bought a certain number of note$-$books for $Rs. 600$ . He sold $\frac{1}{4}$ of them at $5$ percent loss. At what price should he sell the remaining note$-$books so as to gain $10 \%$ on the whole?
Answer$\text{C.P}$. of note$-$books $= Rs. 600$ Gain desired on the whole $=10 \%$
$\therefore$ Total $\text{S.P}$. of all the note$-$books
$=\frac{(100+\text { gain } \%)}{100} \times \text { C.P. }=\left(\frac{100+10}{10}\right) \times Rs. 600$
$ =Rs. \frac{110}{100} \times 600=Rs. 660$
$\text{C.P}$. of $\frac{1}{4}$ of the note$-$books $=\frac{1}{4} \times Rs. 600$
$=Rs. 150$ Loss on these note$-$books $=5 \%$
$\therefore \text{S.P.}$ of this note$-$book
$=\frac{(100-\operatorname{Loss} \%)}{100} \times \text { C.P. }=\frac{(100-5)}{100} \times Rs. 150$
$ =Rs.\frac{95}{100} \times 150$
$ = Rs. \frac{14250}{100}$
$ =Rs.142.50$
Now, $\text{C.P}$. of the remaining note$-$books
$=Rs.600- Rs.150=Rs. 450$
Required $\text{S.P}$. of the remaining note$-$books
$= Rs. 660- Rs.142.50= Rs. 517.50$
View full question & answer→Question 135 Marks
A shop$-$keeper bought rice worth $Rs.4,500$. He sold one$-$third of it at $10\%$ profit. If he desires a profit of $12\%$ on the whole; find : $(i)$ the selling price of the rest of the rice ; $(ii)$ the percentage profit on the rest of the rice.
Answer$\text{C.P}$. of the rice $=Rs. 4500$
Profit desired on the whole $=12 \%$
$\therefore \text{S.P.}$ of the whole rice $=\frac{(100+\text { gain } \%)}{100} \times \text{C.P}$.
$=\frac{(100+12)}{100} \times Rs.4500$
$ = Rs.\frac{112}{100} \times 4500$
$ =112 \times 45=Rs. 5040$
$\text{C.P}.$ of $\frac{1}{3}$ of rice $=\frac{1}{3} \times Rs. 4500$
$=Rs.1500$
Since gain on $\frac{1}{3}$ of rice $=10 \%$
$\therefore \text { S.P.}$ on it $=\left(\frac{100+\text { gain } \%}{100}\right) \times \text { C.P. }$
$=\frac{100+10}{100} \times Rs.1500$
$ =Rs. \frac{110}{100} \times 1500$
$=11 \times 150=Rs.1650$
Remaining $\text{C.P}$. of the rice
$=Rs. 4500- Rs.1500=Rs,.3000$
Remaining $\text{S.P}$. of the rice
$=Rs. 5040 - Rs.1650 = Rs. 3390$
Profit on the remaining rice
$ = Rs. 3390 - Rs. 3000 = Rs. 390$
Gain $\%$ on the remaining rice $=\frac{390}{3000} \times 100$
$=\frac{390 \times 100}{3000}=13 \%$
$\therefore (i)\ \text{S.P}.$ of the rest of the price $= Rs. 3390$
$(ii)\ \%$ profit on the rest of the rice $=13 \%$
View full question & answer→Question 145 Marks
A fruit$-$seller sells $4$ oranges for $Rs. 3$, gaining $50\%$. Find : $(i)\ \text{C.P}.$ of $4$ oranges,$\ (ii)\ \text{C.P}$. of one orange.$\ (iii)\ \text{S.P}.$ of one orange.$\ (iv)\ $ profit made by selling one orange.$\ (v)\ $ a number of oranges brought and sold in order to gain $Rs. 24.$
Answer$\text{S.P}$.of $4$ oranges $= Rs. 3$
$\therefore \text{S.P}$. of $1$ orange $= Rs. \frac{3}{4}$, Gain $=50 \%$
$\text { S.P. }=\frac{\text { C.P. } \times 150}{100}$
$\therefore \text{C.P.}$ of $1$ orange $=\frac{100 \times \text { S.P. }}{(100+50)}$
$\frac{100 \times \frac{3}{4}}{150}=\frac{75}{150}$
$= Rs.\frac{1}{2}$
$(i) \text{C.P}$. of $4$ orange $=4 \times \frac{1}{2}= Rs. 2$
$(ii) \text{C.P}$. of $1$ orange $= Rs. \frac{1}{2}=Rs. (0.50)$
$(iii) \text{S.P.}$ of $1$ orange $= Rs. \frac{3}{4}= Rs. 0.75$
$(iv)$ Profit made by selling one orange
$= Rs. \frac{3}{4}- Rs. \frac{1}{2}= Rs. \frac{1}{4}= Rs. 0.25$
$(v)$ If gain is $Rs. \frac{1}{4}$, number of oranges $=1$
If gain is $Rs. 24,$ number of oranges $=\frac{1}{\frac{4}{1}} \times 24$
$1 \times \frac{4}{1} \times 24=96$
View full question & answer→Question 155 Marks
Renu sold an article at a loss of $8$ percent. Had she bought it at $10\%$ less and sold for $Rs.36$ more; she would have gained $20\%$. Find the cost price of the article.
AnswerLet $\text{C.P}.$ of the article $= Rs. 100$
In the $I$ case :
When loss $=8 \%$
$\text { S.P. }=Rs. (100-8)=Rs. 92$
In the $II$ case :
$\text { C.P. }=\left(100-\frac{10}{100} \times 100\right)$
$ = Rs.(100-10)=Rs.90$
Profit $=20 \%$
$\text { S.P. }=\frac{100+20}{100} \times \text { C.P. }$
$=\frac{120}{100} \times Rs. 90$
$ = Rs.12 \times 9$
$= Rs. 108$
Difference of two selling prices
$=Rs. 108 - Rs. 92 = Rs. 16$
If the difference between the two selling prices is $Rs. 16$ then $\text{C.P}. = Rs. 100$
If the difference between the two selling prices is $Rs. 1$ then $\text{C.P}. = Rs. \frac{100}{16}$
If the difference of two selling prcies is $Rs. 36$ then $\text{C.P}. = Rs. \frac{100}{16} \times 36$
$= Rs. \frac{100 \times 36}{16}$
$ = Rs. 25 \times 9$
$ = Rs. 225$
View full question & answer→Question 165 Marks
A man sold a bicycle at $5\%$ profit. If the cost had been $30\%$ less and the selling price $Rs.63$ less, he would have made a profit of $30\%$. What is the cost price of the bicycle?
AnswerLet $\text{C.P}$. of the bicycle $= Rs. 100$
In the $I$ case :
When Profit $=5 \%$ ；
$\text { S.P}. = Rs. (100+5)=Rs. 105$
In the $II$ case :
$\text { C.P. }=\left(100-\frac{30}{100} \times 100\right)$
$ =Rs.(100-30)=Rs.70$
Profit $=30 \%$
$\text { S.P. }=\frac{(100+\text { Profit })}{100} \times \text { C.P. }$
$=\frac{(100+30)}{100} \times Rs.70$
$ =\frac{130}{100} \times Rs. 70$
$ = Rs. \frac{130 \times 70}{100}$
$= Rs.91$
A difference of two selling prices
$=Rs.105- Rs. 91=Rs. 14$
If the difference is $Rs. 14$ then $\text{C.P}$. of the bicycle $= Rs. 100$ If the difference is $Rs. 1$ then $\text{C.P}$. of the bicycle $= Rs.$
$\frac{100}{14}$
If the difference is $Rs. 63$ then $\text{C.P}$. of the bicycle $= Rs.\frac{100}{14} \times 63$
$=Rs. \frac{100 \times 63}{14}$
$=Rs. 50 \times 9$
$=Rs. 450$
View full question & answer→Question 175 Marks
Mr. Sinha sold two tape$-$recorders for $Rs.990$ each; gaining $10%$ on one and losing $10\%$ on the other. Find his total loss or gain as a percent on the whole transaction.
AnswerIn the case of the first tape$-$recorder:
$\text { S.P. }=Rs. 990$
Gain $=10 \%$
$ \text { C.P. }=\frac{100}{(100+\text { gain } \%)} \times \text { S.P. }$
$ =\frac{100}{(100+10)} \times Rs.990= Rs.\frac{100}{110} \times 990$
$ = Rs.100 \times 9=Rs. 900$
In the case of the second tape$-$recorder:
$\text { S.P}. = Rs. 990$
Loss $=10 \%$
$\text { C.P. }=\frac{100}{(100-\mathrm{Loss} \%)} \times \text { S.P. }$
$ =\frac{100}{(100-10)} \times Rs. 990=\frac{100}{90} \times 990$
$ =100 \times 11=Rs. 1100$
Total $\text {C.P}$. of both the tape$-$recorders
$=Rs. 900+ Rs.1100=Rs. 2000$
Total $\text {S.P}$. of both the tape$-$recorders
$=Rs. 990 + Rs. 990 = Rs.1980$
Loss on the whole transaction
$=\text { C.P. }- \text { S.P. }$
$=Rs. 2000 - Rs. 1980$
$=Rs. 20$
Loss $\%=\frac{\text { Loss }}{\text { C.P. }} \times 100$
$=\frac{\text { Rs. } 20}{\text { Rs. } 2000} \times 100=\frac{2}{2} \%=1 \%$
View full question & answer→Question 185 Marks
By selling a sofa$-$set for $Rs.2,500;$ the shopkeeper loses $20\%$. Find his loss percent or profit percent; if he sells the same sofa$-$set for $Rs.3150.$
AnswerIn the first condition:
$\text{S.P.}$ of a Sofa$-$set $= Rs. 2500$
Loss $=20 \%$
$\therefore \text{C.P.} =\frac{100}{(100-\operatorname{Loss} \%)} \times \text{S.P.}$
$=\frac{100}{(100-20)} \times Rs. 2500$
$= Rs. \frac{100}{80} \times 2500$
$= Rs. \frac{100 \times 2500}{80}=\frac{5 \times 2500}{4}=5 \times 625$
$= Rs. 3125$
In the second condition:
$\text{S.P.}$ of the Sofa$-$set $= Rs. 3150$
$\text{C.P.}$ of the sofa$-$set $= Rs. 3125$
Gain $= \text{S.P.} - \text{C.P.} = Rs. 3150- Rs. 3125= Rs. 25$
Gain $\%=\frac{\text { Gain }}{\text {{C.P.} }} \times 100$
$=\frac{25}{3125} \times 100=\frac{25 \times 100}{3125}=\frac{100}{125}$
$=\frac{4}{5} \%=0.8 \%$
View full question & answer→Question 195 Marks
A man sells a radio-set for $Rs.605$ and gains $10\%$. At what price should he sell another radio of the same kind, in order to gain $16\%?$
AnswerIn the first condition:
$\text { S.P.}$ of a radio$-$set $= Rs. 605$
Gain $=10 \%$
$\text { C.P.} =\frac{100}{(100+\text { gain } \%)} \times \text { S.P.}$
$=\frac{100}{(100+10)} \times Rs. 605$
$= Rs. \frac{100}{110} \times 605$
$= Rs. \frac{100 \times 605}{110}$
$=10 \times 55$
$= Rs. 550$
In the second condition:
$\text { C.P. }= Rs. 550$
Gain $=16 \%$
$ \text { S.P. }=\frac{(100+\text { gain } \%)}{100} \times \text { C.P. }$
$ =\frac{(100+16)}{100} \times \text { Rs. } 550$
$ = Rs. \frac{116}{100} \times 550$
$ = Rs. \frac{116 \times 550}{100}$
$ =58 \times 11$
$ = Rs. 638$
$\therefore$ Radio should be sold at $Rs. 638 .$
View full question & answer→Question 205 Marks
John sold an article to Peter at $20\%$ profit and Peter sold it to Mohan at $5\%$ loss. If Mohan paid $Rs.912$ for the article; find how much did John pay for it?
AnswerMohan paid for the article $= Rs. 912$
$\because$ Peter sold the article to Mohan
$\therefore$ For peter :
$\text { S.P. }= Rs. 912$
Loss $=5 \%$
$\text { C.P. }=\frac{100}{(100-\operatorname{Loss} \%)} \times \text { S.P. }$
$=\frac{100}{(100-5)} \times Rs. 912$
$=Rs. \frac{100 \times 912}{95}$
$=20 \times 48=Rs. 960$
John sold the same article to Peter
$\therefore$ For John :
$\text { S.P}. = Rs. 960$
Profit $=20 \%$
$\text { C.P. }=\frac{100}{(100+\text { Profit } \%)} \times \text { S.P. }$
$=\frac{100}{(100+20)} \times Rs. 960$
John sold the same article to Peter
$\therefore$ For John :
$\text { S.P}. = Rs. 960$
Profit $=20 \%$
$\text { C.P. }=\frac{100}{(100+\text { Profit\% })} \times \text { S.P. }$
$ =\frac{100}{(100+20)} \times Rs. 960$
$ = Rs. \frac{100}{120} \times 960$
$ = Rs. 100 \times 8= Rs. 800$
Hence, John paid for article $= Rs. 800$
View full question & answer→Question 215 Marks
Rajesh sold his scooter to Rahim at $8\%$ loss and Rahim, in turn, sold the same scooter to Prem at $5\%$ gain. If Prem paid $Rs. 14,490$ for the scooter; find : $(i)$ the $\text{S.P}$. and the $\text{C.P}$. of the scooter for Rahim $(ii)$ the $\text{S.P}.$ and the $\text{C.P}$. of the scooter for Rajesh
AnswerLet $\text{C.P}$. of the scooter for Rajesh$ = Rs. 100 \mathrm{x}$
$\text{S.P}$. for Rajesh $=\frac{100 \mathrm{x} \times 92}{100}=92 \mathrm{x}$
This will be $\text{C.P}$. for Rahim $=92 x$, Gain $=5 \%$
$\therefore \text{S.P}$. for Rahim $=\frac{92 \mathrm{x} \times 105}{100}$
$=\frac{92 \mathrm{x} \times 21}{20}=\frac{46 \mathrm{x} \times 21}{10}=\frac{966 \mathrm{x}}{10}$
This will be $\text{C.P}$. for Prem $= Rs. 14,490$
$\therefore \frac{966 \mathrm{x}}{10}=14,490$
$ \Rightarrow \mathrm{x}=\frac{14490}{966} \times 10=\frac{14490}{483} \times 5=30 \times 5=150$
$(i) \text{C.P}$. of scooter for Rahim $=92 \mathrm{x}=92 \times 150$
$=\text { Rs. } 13800$
$\text{S.P}$. of scooter for Rahim $=\frac{966 \mathrm{x}}{10}=\frac{966}{10} \times 150$
$\text { = Rs. } 966 \times 15=\text { Rs. } 14490$
$(ii) \therefore \text{C.P}$. of Scooter for Rajesh $=100 \mathrm{x}=100 \times 150$
$=\text { Rs. } 15000$
$\text{S.P}$. of scooter for Rajesh $= 92x = Rs. 92 \times 150$
$= Rs. 13800$
View full question & answer→Question 225 Marks
A tape$-$recorder is sold for $Rs. 2,760$ at a gain of $15\%$ and a $C.D$. player is sold for $Rs. 3,240$ at a loss of $10\%$ Find : $ (i)$ the $\text{C.P}$. of the tape$-$recorder$\ (ii)\ $ the $\text{C.P}$. of the $C.D$. player.$\ (iii)\ $ the total $\text{C.P}$. of both.$\ (iv)\ $ the total $\text{S.P}$. of both$\ (v)$ the gain $\%$ or the loss $\%$ on the whole
Answer$\text{S.P}$. of tape$-$recorder $= Rs. 2,760$
Gain $=15 \%$
$(i) \text{C.P} =\frac{100 \times { \text{S.P}. }}{115} \ldots . . .\left[\right. \text{C.P} \left.=\frac{100 \times { \text{S.P}. }}{(100+\text { Gain })}\right]$
$=\frac{100 \times 2760}{115}=\frac{20 \times 2760}{23}=20 \times 120=\text { Rs. } 2400$
$(ii) \text{S.P}$. of $\text{C.D}$. Player $= Rs. 3,240$
${\left[ { \text{C.P} }=\frac{100}{(100$-$\text { loss })} \times { \text{S.P}. }\right]}$
$ =\frac{100}{(100$-$10)} \times 3240$
$ =\frac{100}{90} \times 3240$
$ =100 \times 36$
$ =\text { Rs. } 3600$
$(iii)$ Total $\text{C.P}$ of both $= Rs. 2400+ Rs. 3600= Rs. 6000$
$(iv)$ Total $\text{S.P}$. of both $= Rs. 2760+ Rs.3240= Rs. 6000 $
$(v)$ Since $\text{S.P} = \text{C.P}$
there is no gain and loss on the whole.
View full question & answer→Question 235 Marks
A man buys a certain number of articles at $15$ for $Rs. 112.50$ and sells them at $12$ for $Rs.108.$ Find ;
$(i)$ his gain as percent ;$(ii)$ the number of articles sold to make a profit of $Rs.75.$
AnswerLet the number of articles bought $= 60$
Note : $\text{L.C.M.}$ of $15$ and $12 = 60$
$\therefore \text { C.P.}$ of the articles $= Rs. \frac{112.50}{15} \times 60$
$= Rs. \frac{112.50 \times 60}{15}=112.50 \times 4$
$= Rs. 450.00$
and $S.P.$ of the articles $= Rs. \frac{108}{12} \times 60$
$= Rs. 108 \times 5 = Rs. 540$
$(i)$ Gain $= S.P. − C.P.$
$= Rs. 540 − Rs. 450$
$= Rs. 90$
$\therefore \text { Gain } \%=\frac{\text { Gain }}{\text { C.P. }} \times 100$
$=\frac{90}{450} \times 100=\frac{100}{5}=20 \%$
$(ii)$ To make a profit of $Rs.90$, the number of articles needed to be sold $= 60$
To make a profit of $Rs. 1$ the number of articles needed to be sold $=\frac{60}{90}$
To make a profit of $Rs.75$, the number of articles needed to be sold
$=\frac{60}{90} \times 75=\frac{4500}{90}=50$
View full question & answer→Question 245 Marks
A man sold a radio$-$set for $Rs.250$ and gained one$-$ninth of its cost price. Find ; $(i)$ its cost price; $(ii)$ the profit percent.
Answer$(i)$ Let $\text{C.P.}$ of the radio$-$set $= Rs.x$
$\text { Gain }=Rs. \frac{x}{9}$
$ \text { S.P. }=Rs. \left(x+\frac{x}{9}\right)=\left(\frac{9 x+x}{9}\right) Rs. =Rs. \frac{10 x}{9}$
But, we are given $\text{S.P.}$ of the radio$-$set $= Rs. 250$
$\therefore \frac{10 \mathrm{x}}{9}=250$
$ \Rightarrow \mathrm{x}=250 \times \frac{9}{10}$
$ \Rightarrow \mathrm{x}=25 \times 9 $
$\Rightarrow \mathrm{x}=225$
$\therefore \text{C.P.}$ of the radio set $= Rs. 225$
$(ii)$ Profit $= Rs. \frac{\mathrm{x}}{9}$
$= Rs. \frac{225}{9} \ldots . .($ Substituting the value of $x)$
$=Rs. 25$
Profit $\%=\frac{\text { Profit }}{\text { C.P. }} \times 100$
$=\frac{25}{225} \times 100=\frac{25 \times 100}{225}=\frac{100}{9} \%$
$=11 \frac{1}{9} \%$
View full question & answer→Question 255 Marks
A man sold his bicycle for $Rs.405$ losing one-tenth of its cost price, find :
$(i)$ its cc price; $(ii)$ the loss percent.
Answer$(i)$ Let $\text {C.P.}$ of the bicycle $= Rs. x$
$\therefore \text { Loss }= Rs. \frac{\mathrm{x}}{10}$
$ \text { S.P. }=\text { C.P. }- \text { Loss }$
$ =\mathrm{x}-\frac{\mathrm{x}}{10}$
But, we are given $\text {S.P.} = Rs. 405$
$\therefore \mathrm{x}-\frac{\mathrm{x}}{10}=405$
$\Rightarrow \frac{10 x-x}{10}=405$
$ \Rightarrow \frac{9 x}{10}=405$
$ \Rightarrow x=405 \times \frac{10}{9}$
$ \Rightarrow x=\frac{4050}{9}$
$\Rightarrow x=450$
$\therefore \text { C.P. }= Rs. 450$
$(ii)$ Loss $=\frac{\mathrm{x}}{10}$
$=\frac{450}{10} \ldots .($ substituting the value of $x)$
$ \text { (ii) Loss }=\frac{\mathrm{x}}{10}$
$ =\frac{450}{10} \ldots($substituting the value of $ \mathrm{x})$
$ = Rs. 45$
$ \text { Loss } \%=\frac{\text { Loss }}{\text { C.P. }} \times 100$
$ =\frac{45}{450} \times 100=\frac{4500}{450}=10 \%$
View full question & answer→