Question 14 Marks
For both the following inter$-$state transaction of services, find the total amount of bill.$(i)$ Cost of services $= 5,000$, discount $= 20\%$ and $\text{GST} = 12\%$$(ii)$ Cost of services $= 12,500$, discount $= 40\%$ and $\text{GST} = 18\%$
Answer$(i)$ Service $1$ Cost $= Rs. 5000$
Discount $=\frac{20}{100} \times 5000= Rs. 1000$
Service Cost after Discount $= Rs. 5000 - Rs. 1000= Rs. 4000$
$\text{IGST}=\frac{12}{100} \times 4000= Rs. 480$
Total amount of bill for Service $1= Rs. 4000+480=4480$
$(ii)$ Service $2$ Cost $= Rs. 12500$
Discount $=12500 \times \frac{40}{100}= Rs. 5000$
Service Cost after Discount $= Rs.12500-5000=7500$
$\text { IGST }=\frac{18}{100} \times 7500=\text { Rs. } 1350$
Total Amount of bill for Service $2= Rs.7500+1350= Rs. 8850$
Total bill $=$Service $1+$ Service $2$
$=4480+8850$
$=Rs.13,330$
View full question & answer→Question 24 Marks
A shopkeeper sells an article for $Rs. 21384$ including $10\%$ sales tax. However, the actual rate of sales tax is $8\%$. Find the extra profit made by the dealer.
AnswerPrice of the article inclusive of sales tax $= Rs. 21,384$
Let $y$ be the list price of the article
Rate of sales tax charged by the shopkeeper $=10 \%$
According to the given statement, we have
$y+\left(y \times \frac{10}{100}\right)=21384$
$ \Rightarrow y+\frac{y}{10}=21384$
$ \Rightarrow \frac{11 y}{10}=21384$
$ \Rightarrow y=\frac{21384 \times 10}{11}$
$ \Rightarrow y=R s .19440$
When the sales tax is $8 \%$, the actual sale price
$=19440+19440 \times \frac{8}{100}$
$ =19440+1555.2=\text { Rs. } 20,995.2$
Extra profit $=$ Sale price of the article charged by shopkeeper $-$ Actual sale price
$\Rightarrow$ Extra profit $= Rs. 21,384 - Rs. 20.995 .2= Rs. 388.80$
View full question & answer→Question 34 Marks
The price of a washing machine, inclusive of sales tax is $Rs.13,530/-$. If the sales tax is $10\%$, find its basic cost price.
AnswerThe selling price of washing machine $= Rs.13,530$
Rate of sales operatorname tax$=7\%$
$\therefore$ Cost price $=\frac{\text { Selling price } \times 100}{(100+\text { Rate of sales tax })}$
$=\frac{13530 \times 100}{100+10}$
$=\frac{1353000}{110}$
$=Rs.12300$
View full question & answer→Question 44 Marks
By selling an article at a $20\%$ discount, a shopkeeper gains $25\%$. If the selling price of the article is $Rs.1,440$; find :$(i)$ the marked price of the article.$(ii)$ the cost price of the article.
Answer$(i) \text{S.P}$. of the article $=Rs. 1440$
Let marked price $= Rs.100 \mathrm{x}$
Discount $=20 \%$
$\therefore \text { S.P. }=\frac{100 \mathrm{x}(100-20)}{100}=80 \mathrm{x}$
According to statement, $80 x=1440$
$x=\frac{1440}{80} \Rightarrow x=18$
$\therefore x=18$
$\therefore$ Marked price $=100 \mathrm{x}=100 \times 18= Rs. 1800$
$(ii) \text{S.P}. = Rs. 1440$
Profit $=25 \%$
$\therefore \text { C.P. }=\frac{100 \times \mathrm{S} . \mathrm{P} .}{100+25}=\frac{100 \times 1440}{125}$
$=\frac{4}{5} \times 1440$
$ =4 \times 288$
$=\text { Rs. } 1152$
View full question & answer→Question 54 Marks
An article is marked at $Rs. 2,250$. By selling it at a discount of $12\%$, the dealer makes a profit of $10\%$. Find $:(i)$ the selling price of the article.$(ii)$ the cost price of the article for the dealer.
Answer$(i)$ Marked price $= Rs. 2,250$
$ \text { S.P. }=\frac{2250(100-12)}{100}$
$ =\frac{2250 \times 88}{100}$
$ =45 \times 44$
$ =\text { Rs. } 1980$
$(ii) \text{S.P}.= Rs. 1980$ , Profit $=10 \%$
$\therefore \text{C.P}$ of the article $=\frac{100}{110} \times 1980$
$=100 \times 18$
$ =\text { Rs. } 1800$
View full question & answer→Question 64 Marks
Find a single discount $($as a percent$)$ equivalent to following successive discounts: $20\%, 10\%$ and $5\%$
AnswerSuccessive discount $= 20\%, 10\%$ and $5\%$
Let $\text{M.P}.= ₹100$
$\therefore \text{S.P}$. after three discounts
$\therefore \text{S.P}. =\frac{\text { M.P. }(100-\text { Discount } \%)}{100}$
$=\text {₹}$$\frac{100(100-20)(100-10)(100-5)}{100 \times 100 \times 100}$
$=\text {₹}$$\frac{100 \times 80 \times 90 \times 95}{100 \times 100 \times 100}$
$=\text {₹}$$\frac{342}{5}$
Total discount $=100-\frac{342}{5}$
$=\frac{500-342}{5}=\frac{158}{5}$
Single discount $=\frac{158}{5} \%$
$= 31.6\%$
View full question & answer→Question 74 Marks
Find a single discount $($as a percent$)$ equivalent to following successive discounts : $ 10%, 20%$ and $20%$
AnswerSuccessive discount $= 10\%, 20\%$ and $20\%$
Let $\text{M.P}.= ₹100$
$\therefore \text{S.P}$. after $3$ discounts
$\therefore \text{S.P}.=\frac{\text { M.P. }(100-\text { Discount } \%)}{100}$
$=\frac{100 \times(100-10)(100-20)(100-20)}{100 \times 100 \times 100}$
$=\frac{100 \times 90 \times 80 \times 80}{100 \times 100 \times 100}=\frac{576}{10}$
$\therefore$ Total discount $=\text {₹} 100$$-\frac{576}{10}$
$=\text {₹}$$\frac{1000-576}{10}=\frac{424}{10}$
$\therefore$ Single discount$=\frac{424}{10} \%$
$= 42.4\%$
View full question & answer→Question 84 Marks
Find a single discount $($as a percent$)$ equivalent to following successive discounts: $20\%$ and $12\%$
AnswerSuccessive discount $= 20\%$ and $12\%$
Let $\text{M.P}. = ₹100$
First discount $= 20\%$
Second discount $= 12\%$
$\therefore \text { S.P. }=\frac{\text { M.P. }(100-\text { Discount %) }}{100} $
$ =\frac{100 \times(100-20)(100-12)}{100 \times 100} $
$ =\frac{100 \times 80 \times 88}{100 \times 100}=\frac{352}{5}$
$\therefore$ Total discount on $₹100 = 100-\frac{352}{5}$
$=\frac{500-352}{5}=\text {₹}\frac{148}{5}$
$\therefore$ Single discount $=\frac{148}{5} \% $
$ =29 \frac{3}{5} \%$
View full question & answer→Question 94 Marks
The cost price of an article is $25\%$ below the marked price. If the article is available at a $15\%$ discount and its cost price is $ Rs.2,400;$ find:$(i)$ Its marked price $(ii)$ its selling price $(iii)$ the profit percent.
AnswerLet $\text{M.P}$. of an article $= ₹100$
$\therefore$ Cost price $=\frac{100 \times(100-25)}{100}$
$=\text {₹}$$\frac{100 \times 75}{100}=$$=\text {₹} 75$
Discount $= 15\%$
$\therefore \text{S.P}. = ₹100 − 15 = ₹85$
But cost price $= ₹2400$
$(i)\therefore$ Marked price$=\text {₹}2400 \times \frac{100}{75} = ₹32 \times 100 = ₹3200$
$(ii)$ and $\text{S.P}.=\text {₹}\frac{3200 \times 85}{100}=\text {₹}2720$
$(iii)$ Profit $=\text{S.P} − \text{C.P}. = ₹2720 − 2400 = ₹320$
$\therefore \text { Profit } \%=\frac{\text { Profit } \times 100}{\text { C.P. }}$
$=\frac{320 \times 100}{2400}$
$=\frac{40}{3} \%$
$=13 \frac{1}{3} \%$
View full question & answer→Question 104 Marks
At $12\%$ discount, the selling price of a pen is $Rs. 13.20.$ Find its marked price. Also, find the new selling price of the pen, if it is sold at $5\%$ discount.
AnswerSelling Price of a Pen $= 13.20$
Discount $= 12\%$
Marked Price =Selling Price $\times\left(\frac{100}{100-d}\right)$
$ =13.20 \times\left(\frac{100}{100-12}\right)$
$ =\frac{1320}{100} \times \frac{100}{88}$
Marked Price $= ₹ 15$
New Discount $= 5\%$
Selling Price = Market Price $ \times\left(\frac{100-d}{100}\right)$
$ =15 \times\left(\frac{100-5}{100}\right)$
$=15 \times \frac{95}{100}$
$=3 \times \frac{19}{4}$
New Selling Price $= ₹ 14.25$
View full question & answer→Question 114 Marks
The cost price of $20$ articles is the same as the selling price of $16$ articles. Find the gain percent.
Answer$\text{C.P}$. of $20$ articles $= \text{S.P}.$ of $16$ articles.
Let $\text{C.P}$. of $1$ article $= Rs. 1$
$\text{C.P}$. of $20$ articles $= Rs. 20$
and $\text{C.P}$. of $16$ articles $= Rs. 16$
$\text{S.P}$. of $16$ articles $= Rs. 20 ..\text{S.P}.$ of $16$ articles $=\text{C.P}$. of $20$ articles
Gain $= Rs. 20- Rs.16= Rs. 4$
Gain $\%=\frac{4}{16} \times 100$
$ =\frac{4 \times 100}{16}$
$ =25 \%$
View full question & answer→Question 124 Marks
A man sells $12$ articles for $Rs. 80$ gaining $33 \frac{1}{3} \%$. Find the number of articles bought by the man for $Rs. 90$.
Answer$S.P$. of $12$ articles $=Rs. 80$ ,
Gain $=33 \frac{1}{3} \%=\frac{100}{3} \%$
$ \text { C.P. }=\frac{100}{(100+\text { Gain })} \times \text { S.P. }$
$ =\frac{100}{100+\frac{100}{3}} \times 80=\frac{100}{\frac{300+100}{3}} \times 80$
$=\frac{100}{\frac{400}{3}} \times 80=100 \times \frac{3}{400} \times 80=\text { Rs. } 60$
$Rs. 60$ is the cost of $12$ articles
$Rs. 1$ is the cost of $=\frac{12}{60}$ article
$Rs. 90$ is the cost of $=\frac{12}{60} \times 90$
$=\frac{1}{5} \times 90=18$
Man can buy an article for $Rs. 90=18$
View full question & answer→Question 134 Marks
A stationery buys pens at $5$ for $Rs.28$ and sells them at a profit of $25\%$. How much should a customer pay; if he buys $(i)$ only one pen $;(ii)$ three pens?
AnswerFor Stationery :
$\text{C.P}$. of $5$ pens $=Rs. 28$
$\text{C.P}$. of $1$ pen $=\frac{28}{5} Rs.= Rs. 5.60$
profit $=25 \%$
$\therefore \text{S.P}$. of $1$ pen
$=\frac{(100+\text { Profit } \%)}{100} \times \text{C.P}$. of $1$ pen
$=\frac{(100+25)}{100} \times Rs. 5.60$
$=Rs. \frac{125}{100} \times 5.60$
$= Rs. \frac{125 \times 5.6}{100}= Rs.5 \times 1.4= Rs. 7$
$\text{S.P}$. of $3$ pens $=3 \times 7= Rs. 21$
$\therefore$ Customer pays for
$(i)$ only one pen $= Rs.7$
$(ii)$ Three pens $= Rs. 21$
View full question & answer→Question 144 Marks
By selling an article for $Rs.704$; a person loses $12\%$. Find his cost price and the loss.
Answer$\text{S.P}$. of an article $= Rs. 704$
Loss $=12 \%$
$\text{C.P}.=\frac{100}{(100-\operatorname{Loss} \%)} \times \text{S.P}.$
$=\frac{100}{(100-12)} \times Rs. 704$
$=Rs. \frac{100}{88} \times 704$
$=Rs. 100 \times 8= Rs. 800$
Loss $= \text{C.P. - S.P}.$
$= Rs. 800-Rs. 704$
$= Rs. 96$
View full question & answer→Question 154 Marks
By selling an article for $Rs.900$; a man gains $20\%$. Find his cost price and the gain.
Answer$\text{S.P}$. of an article $= Rs. 900$
Gain $=20\% \ \text{C.P}.=\frac{100}{(100+\text { Gain } \%)} \times \text{S.P}.$
$\therefore \text{C.P}. =\frac{100}{(100+20)} \times Rs. 900$
$= Rs.\frac{100}{120} \times 900$
$= Rs.\frac{9000}{12}$
Gain $= \text{S.P. - C.P}.$
$= Rs. 900- Rs. 750$
$= Rs. 150$
View full question & answer→Question 164 Marks
The cost price of an article is $\frac{4}{5}$ times of its selling price. Find the loss or the gain as a percent.
AnswerLet $\text{S.P}. =1$
$\text{ C.P. }=\frac{4}{5} \times 1=\frac{4}{5}$
$\therefore$ Gain $= \text{S.P. - C.P}. ...... [\because$ Gain $= \text{S.P. - C.P}.]$
$=1-\frac{4}{5}=\frac{5-4}{5}=\frac{1}{5}$
$\therefore$ Gain $\%=\frac{\text { Gain }}{\text { C.P. }} \times 100$
$=\frac{\frac{1}{5}}{\frac{4}{5}} \times 100$
$=\frac{1}{5} \times \frac{5}{4} \times 100=25 \%$
View full question & answer→Question 174 Marks
A fruit$-$seller buys oranges at $4$ for $Rs.3$ and sells them at $3$ for $Rs.4$ Find his profit percent.
AnswerLet number of oranges bought $=12$
$[$Note: $\text{L.C.M}$. of $4$ and $3=12]$
$\therefore \text{C.P}$. of oranges $=Rs. \frac{3}{4} \times 12= Rs.9$
and $\text{S.P.}$ of oranges $= Rs.\frac{4}{3} \times 12$
$= Rs. 16$
$\therefore$ Profit $=16-9$
$=Rs. 7$
Profit $\%=\frac{\text { Profit }}{\text { C.P. }} \times 100$
$=\frac{7}{9} \times 100=\frac{700}{9} \%$
$=77 \frac{7}{9} \%$
View full question & answer→Question 184 Marks
Megha bought $10$ note$-$books for $Rs.40$ and sold them at $Rs.4.75$ per note$-$book. Find, her gain percent.
Answer$\text{C.P}$. of $10$ note$-$books $= Rs. 40$
$\text{S.P}.$ of $10$ note$-b$ooks $@Rs. 4.75$ per note$-$book
$=4.75 \times 10=\text { Rs. } 47.50$
Gain $=\text { S.P. }- \text { C.P. }$
$ =Rs.47.50-Rs.40=Rs.7.50$
Gain $\%=\frac{\text { Gain }}{\text { C.P. }} \times 100$
$ =\frac{7.50}{40} \times 100=\frac{750}{40} \%$
$ =\frac{75}{4} \%$
$ =18 \frac{3}{4} \%$
View full question & answer→Question 194 Marks
A shop$-$keeper bought $300$ eggs at $80$ paise each. $30$ eggs were broken in a transaction and then he sold the remaining eggs at one rupee each. Find, his gain or loss as a percent.
Answer$\text{C.P}.$ of $300$ eggs $@ 80$ paise each
$=300 \times 80=24000$ paise $=Rs.240$
No. of eggs which were broken in transaction $=30$
Remaining eggs $=300-30$
$=270$
$\text{S.P}$. of eggs $@ Rs. 1$ each $=270 \times 1= Rs. 270$
Gain $=\text { S.P. }- \text { C.P. }$
$=\text { Rs. } 270-\text { Rs. } 240=\text { Rs. } 30$
Gain $\% =\frac{\text { Gain }}{\text { C.P. }} \times 100$
$=\frac{30}{240} \times 100$
$ =\frac{100}{8} \%=12.5 \%$
View full question & answer→Question 204 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 $=82400+9888=\operatorname{Rs} 92288$
View full question & answer→Question 214 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
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 $\text{GST}$
$=7200+2016=Rs. 9216$
View full question & answer→Question 224 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 234 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}= Rs. 26000$
Thus the list price of the T.V is $Rs. 26000$
View full question & answer→Question 244 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 254 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
$y+9 \% \text { of } y=\text { Rs }.13407$
$ \Rightarrow y+\frac{9 y}{100}=\text { Rs. } 13407$
$ \Rightarrow \frac{109 y}{100}=\text { Rs. } 13407$
$ \Rightarrow y=\frac{13407 \times 100}{109}=\text { Rs. } 12300$
New rate of sales $\operatorname{tax}=13 \%$
New total price for $T.V. = Rs. 12,300+13 \%$ of $Rs. 12,300$
$=\text { Rs. } 12300+\frac{13}{100} \times 12300$
$ =\text { Rs. } 12300+\text { Rs. } 1599$
$=\text { Rs. } 13899$
More money paid $= Rs. 13,899 - Rs. 13,407= Rs. 492$
View full question & answer→Question 264 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+\text { Rs } 31.86$
$ =Rs.385.86$
Total amount paid by Sarita $= Rs. 167.48 + Rs. 385.86$
$=\text { Rs. } 553.34$
View full question & answer→Question 274 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 284 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 294 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
Loss of $= 6\%= ₹450 \times 30 = ₹13500$
$\text{C.P}$. of $\frac{1}{3}$ articles $=\text {₹} 450$$\times \frac{30}{3}$
$= ₹4500$
$\therefore \text{S.P}$. of $10$ articles $= \frac{\text { C.P. } \times(100-\text { Loss } \%)}{100}$
$=\text {₹}$$\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
$=\text {₹}\frac{13500 \times(100+10)}{100}$
$=\text {₹}\frac{13500 \times 110}{100}$
$= ₹14850$
$\therefore \text{S.P}.$ of the remaining $20$ articles.
$= ₹14850 − ₹4230 = ₹10620$
$\therefore \text{S.P}$. of $1$ article $=\text {₹}\frac{10620}{20}=\text {₹}531$
View full question & answer→Question 304 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 $\text{M.P}. = ₹.100$
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 314 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 324 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 334 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 344 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 354 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 364 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 374 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 $=20 \%$
$\therefore \text{C.P}. =\frac{100}{(100-\operatorname{Loss} \%)} \times S.P.$
$=\frac{100}{(100-20)} \times Rs. 2500$
$= Rs. \frac{100}{80} \times 2500$
$= Rs.\frac{100 \times 2500}{80}=\frac{5 \times 2500}{4}=5 \times 625$
$=Rs. 3125$
In the second condition:
$S.P$. of the sofa$-$set $= Rs. 3150$
$C.P.$ of the sofa$-$set $= Rs. 3125$
Gain $= \text{S.P. - C.P.} = Rs. 3150- Rs. 3125= Rs. 25$
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 384 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 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 394 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 404 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 $=92 \mathrm{x}=92 \times 150$
$= Rs.13800$
$\text{S.P}$. of scooter for Rahim $=\frac{966 \mathrm{x}}{10}=\frac{966}{10} \times 150$
$= Rs. 966 \times 15= Rs.14490$
$(ii) \therefore \text{C.P}$. of Scooter for Rajesh $=100 \mathrm{x}=100 \times 150$
$=Rs. 15000$
$\text{S.P.}$ of scooter for Rajesh $= 92x = Rs. 92 \times 150$
$= Rs. 13800$
View full question & answer→Question 414 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 $C.D$. 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 $\text{S.P. = C.P}$.
there is no gain and loss on the whole.
View full question & answer→Question 424 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 $=\text { Rs. } \frac{112.50}{15} \times 60$
$=\text { Rs. } \frac{112.50 \times 60}{15}=112.50 \times 4$
$= Rs. 450.00$
and $\text{S.P}$. of the articles $= Rs. \frac{108}{12} \times 60$
$= Rs. 108 \times 5 = Rs. 540$
$(i)$ Gain $= \text{S.P. − C.P}$.
$= Rs. 540 − Rs. 450$
$= Rs. 90$
$\therefore$ 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 434 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 $= Rs.x$
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 444 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 $= Rs. x$
$\therefore$ Loss $=Rs.\frac{\mathrm{x}}{10}$
$ \text { S.P. }=\text { C.P. }-$ 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 $x)$
$ (iii)$ Loss $=\frac{\mathrm{x}}{10}$
$ =\frac{450}{10} \ldots($substituting the value of $\mathrm{x})$
$ =\text { Rs. } 45$
Loss $ \%=\frac{\text { Loss }}{\text { C.P. }} \times 100$
$ =\frac{45}{450} \times 100=\frac{4500}{450}=10 \%$
View full question & answer→