Question 13 Marks
Find the amount of bill for the following inter$-$state transaction of goods$/$services: Cost of transaction $= 30,000$; discount $= 30\%$ and $\text{GST}=28\%$.
AnswerCost of goods $=Rs. 30000$
Discount $=30 \%$
$=\left(\frac{30}{100}\right) \times 30000$
$= Rs. 9000$
Basic Cost $=30000-9000= Rs. 21000$
$\text{IGST} =\left(\frac{28}{100}\right) \times 21000= Rs. 5880$
Total Amount $=21000+5880= Rs. 26880$
View full question & answer→Question 23 Marks
John belongs to Delhi. He buys goods, worth $Rs. 25,000$ from a shop in Delhi. If the rate of $\text{GST}$ is $5\%$, find how much money in all, will Does John pay for these goods?
AnswerGood Worth $= Rs. 25000$
$\text{CGST} =\left(\frac{2.5}{100}\right) \times 25000=\text { Rs. } 625$
$\text{SGST} =\left(\frac{2.5}{100}\right) \times 25000=\text { Rs. } 625$
Total $\text{GST}= Rs. 625+625=1250$
Total Amount $=25000+1250= Rs. 26250$
View full question & answer→Question 33 Marks
A bicycle is available for $Rs\ 1,664$ including sales tax. If the list price of the bicycle is $Rs\ 1,600$, find :$(1)$ the rate of sales tax.$(2)$ the price, a customer will pay for the bicycle if the sales tax is increased by $6\%$.
AnswerPrice of bicycle inclusive of sales tax $=Rs. 1,664$
List price of bicycle $= Rs.1,600$
$(1)$ Rate of sales tax $=\frac{\text { sales tax }}{\text { list price }} \times 100 \%=\frac{64}{1600} \times 100 \%=4 \%$
$(2)$ New rate of sales tax $=(4+6) \%=10 \%$
New total price $=\text{ Rs}.1,600+10 \% $ of $\text{Rs}. 1,600$
$=\text { Rs. } 1600+\frac{10}{100} \times 1600$
$= Rs. 1600+ Rs. 160$
$= Rs. 1760$
View full question & answer→Question 43 Marks
Ramesh paid $ Rs\ 345.60$ as sales tax on a purchase of $Rs\ 3,840$. Find the rate of sales tax.
AnswerSale price $= Rs\ 3,840$
Sales tax paid $= Rs\ 345.60$
$\therefore$ Rate of sales tax $=\frac{\text { sales } \operatorname{tax}}{\text { sale price }} \times 100 \%$
$=\frac{345.60}{3840} \times 100 \%$
$=9 \%$
View full question & answer→Question 53 Marks
Rajat purchases a wrist-watch costing $Rs\ 540$. The rate of sales tax is $8\%$. Find the total amount paid by Rajat for the watch.
AnswerThe sale price of watch $= Rs\ 540$ Rate of sales $\operatorname{tax}=8 \%$
Total amount paid by Rajat $= Rs \ 540+8 \%$ of $Rs \ 540$
$=Rs\ 540+\frac{8}{100} \times 540$
$ =Rs \ 540+\text { Rs } 43.20$
$ =Rs\ 583.20$
View full question & answer→Question 63 Marks
The list price of an article is $Rs. 800$ and is available at a discount of $15$ percent. Find :$(i)$ selling price of the article;$ (ii)$ cost price of the article, if a profit of $13 \frac{1}{3} \%$ is made on selling it.
AnswerA list price of the article $= Rs. 800$
Discount $@ 15\%$ = $\frac{15}{100} \times Rs. 800$
$= Rs. 120$
$(i)\text{S.P}$. of the article $= Rs. 800- Rs. 120$
$= Rs. 680$
$(ii) \text{S.P}$. of the article $= Rs. 680$
Profit $=13 \frac{1}{3} \%=\frac{40}{3} \%$
$\text{C.P}.=\frac{100}{100+\text { Profit }} \times \text{S.P}.$
$=\frac{100}{100+\frac{40}{3}} \times Rs. 680$
$=\frac{100}{\frac{340}{3}} \times Rs. 680$
$=\frac{3}{340} \times 100 \times 680=3 \times 100 \times 2 Rs$.
$= Rs. 600$
View full question & answer→Question 73 Marks
A shopkeeper sells an article for $Rs. 248.50$ after allowing a discount of $10\%$. Find the list price of the article.
Answer$\text{S.P}$. of the article $= Rs.\ 248.50$
Discount $=10 \%$
Let $\text{M.P}. = Rs. 100$
Discount $=\frac{10}{100} \times Rs. 100=Rs. 10$
Selling price $= Rs. 100- Rs. 10= Rs. 90$
If $\text{S.P}$. is $Rs. 90$ ; then $\text{M.P}. = Rs. 100$
If $\text{S.P}$. is $Rs. 1$ ; then $\text{M.P}. = Rs. \frac{100}{90}$
If $\text{S.P}$. is $Rs.248.50;$ then $\text{ M.P}. = Rs. \frac{100}{90} \times 248.50$
$= Rs. \frac{100 \times 248.50}{90}$
$= Rs. \frac{24850}{90}$
$= Rs.276.11$
$($Approx$)$
View full question & answer→Question 83 Marks
A wrist-watch is available at a discount of $9\%$. If the list-price of the watch is $Rs. 1,400$; find the discount is given and the selling price of the watch.
AnswerA list price of the watch $=Rs. 1,400$
Discount $=9 \%$
Discount $=\frac{1400 \times 9}{100}=14 \times 9= Rs. 126$
$\text{S.P}. =($ List price - Discount $)= Rs. (1400-126)= Rs. 1274$
View full question & answer→Question 93 Marks
Find the single discount $($as a percent$)$ equivalent to successive discounts of: $60\%$ and $80\%$
AnswerSuccessive discounts $= 60\%$ and $80\%$
Let $\text{M.P}. = ₹100$
$\therefore \text{S.P}.$ after two discounts,
$=\text {₹}$$\frac{100(100-60) \times(100-80)}{100 \times 100}$
$=\text {₹}$$\frac{100 \times 40 \times 20}{100 \times 100}$$=\text {₹}80$
$\therefore$ Total discount $= ₹100 − 8 = ₹92$
$\therefore$ Single discount $= 92\%$
View full question & answer→Question 103 Marks
Find the single discount $($as a percent$)$ equivalent to successive discounts of: $ 60\%$ and $60\%$
AnswerSuccessive discounts $= 60\%$ and $60\%$
Let $\text{M.P}. = ₹100$
Then $\text{S.P}$. after two discounts,
$=\text {₹}$$\frac{100(100-60) \times(100-60)}{100 \times 100}$
$=\frac{100 \times 40 \times 40}{100 \times 100}=\text {₹}16$
$\therefore $ Total discount $= ₹100 − 16 = ₹84$
$\therefore $ Single discount $= 84\%$
View full question & answer→Question 113 Marks
Find the single discount $($as a percent$)$ equivalent to successive discounts of: $80\%$ and $80\%$
AnswerSuccessive discounts $= 80\%$ and $80\%$
Let $\text{M.P}. = ₹100$
Then $\text{S.P}$. after two discounts
$=\text {₹}$$\frac{100(100-80) \times(100-80)}{100 \times 100}$
$=\frac{100 \times 20 \times 20}{100 \times 100}$$=\text {₹} 4$
$\therefore$ Total discount $= ₹100 − 4 = ₹96$
$\therefore$ Single discount $= 96\%$
View full question & answer→Question 123 Marks
The cost price of an article is $Rs. 2,400$ and it is marked at $25\%$ above the cost price. Find the profit and the profit percent, if the article is sold at a $15\%$ discount.
Answer$\text{C.P}. = ₹2,400$
$\therefore$ Marked price $=\frac{2400(100+25)}{100}$
$= 24 \times 125$
$= ₹3000$
Discount $= 15\%$
$\therefore \text{S .P} .=\frac{3000 \times(100-15)}{100}$
$= 30 \times 85$
$= ₹2550$
$\therefore$ Profit$ = ₹2550 − ₹2400$
$= ₹150$
Profit $\%=\frac{150}{2400} \times 100=\frac{50}{8}=\frac{25}{4}$
$=6 \frac{1}{4} \%$
View full question & answer→Question 133 Marks
Raju sells a watch at a $5\%$ profit. Had he sold it for $Rs.24$ more; he would have gained $11\%$. Find the cost price of the watch.
AnswerLet $\text{C.P}$ of the watch $= Rs. 100$
When profit $=5 \% ;\text{S.P} = Rs.(100+5)= Rs.105$
When profit $=11 \%$;
$\text{S.P}.= Rs(100+11)=Rs .111$
Difference of two selling prices $= Rs.111 - Rs.105=Rs. 6$
When watch sold for $Rs. 6$ more; then $\text{C.P}$. of the watch $= Rs. 100$
When watch sold for $Rs.1$ more; then $\text{C.P}$. of the watch $= Rs. \frac{100}{6}$
When watch sold for $Rs.24$ more; then $\text{C.P}$ of the watch $= Rs. \frac{100}{6} \times 24$
$=\text { Rs. } 400$
View full question & answer→Question 143 Marks
The selling price of $15$ articles is equal to the cost price of $12$ articles. Find the gain or loss as a percent.
Answer$\text{S.P}$. of $15$ articles $= \text{C.P}$. of $12$ articles
Let $\text{C.P}.$ of $1$ article $= Rs.1$
$\text{C.P}$. of $12$ article $= Rs. 12$
and $\text{C.P}$. of $15$ articles $= Rs.15$
$\text{S.P}$. of $15$ articles $= Rs. 12 \ldots$ $[\text{S.P}$. of $15$ articles $= \text{C.P}$. of $12$ articles$]$
Loss $= Rs. 15- Rs. 12= Rs. 3$
Loss $\%=\frac{3}{15} \times 100=20 \%$
View full question & answer→Question 153 Marks
If John sells his bicycle for $ Rs. 637$, he will suffer a loss of $9\%$. For how much should it be sold, if he desires a profit of $5\%$?
Answer$\text { S.P. }=\text Rs. 637$
Loss $=9 \%$
$ \therefore \text { C.P. }=\frac{100 \times \text { S.P. }}{100-9}$
$ =\frac{100}{91} \times 637$
$ =100 \times 7$
$ =\text { Rs. } 700$
Profit $=5 \%$
$\text { S.P. }=\frac{(100+\text { Profit })}{100} \times \text { C.P. }$
$\text { S.P. }=\frac{(100+5)}{100} \times 700$
$ =105 \times 7$
$ =735$
View full question & answer→Question 163 Marks
Find the selling price, if : $\text{C.P}. = Rs.576$; overheads $= Rs.44$ and loss$ = 16\%$
Answer$\text { C.P. }=\text { Rs. } 576$
Overheads $= Rs. 44$
Net $\text{C.P}. = Rs. 576+ Rs. 44$
$=\text { Rs. } 620$
Loss$=16 \%$
We know : $\text{S.P}.=\frac{(100-\operatorname{Loss} \%)}{100} \times \text{C.P}.$
$=\frac{(100-16)}{100} \times \text { Rs. } 620$
$ =\text { Rs. } \frac{84}{100} \times 620$
$ =\text { Rs. } \frac{5208}{10}$
$ =\text { Rs. } 520.80$
View full question & answer→Question 173 Marks
Find the selling price, if :$\text{C.P}.= Rs.352;$ overheads$ = Rs.28$ and profit $= 20$
Answer$\text{C.P.}=Rs.352$
Overheads $= Rs. 28$
Net $\text{C.P}.= Rs. 352+ Rs.28=Rs.380$
Profit $=20 \%$
We know: $\text{S.P}. =\frac{(100+\text { gain } \%)}{100} \times\text{C.P.}$
$=\frac{(100+20)}{100} \times \text { Rs. } 380$
$ =\text { Rs. } \frac{120}{100} \times 380$
$ =12 \times 38$
$ =\text { Rs. } 456$
View full question & answer→Question 183 Marks
Find the cost price, if :$\text{S.P}.= Rs.1,128$ and loss $= 6\%$
Answer$ \text { S.P. }=\text { Rs. } 1,128$
$\text { loss }=6 \%$
$ \text { C.P. }=\frac{100}{(100-\text { loss })} \times \text { S.P. }$
$ \therefore \text { C.P. }=\frac{100 \times 1128}{(100-6)}=\frac{100 \times 1128}{94}$
$ =100 \times 12$
$ =\text { Rs. } 1200$
View full question & answer→Question 193 Marks
Find the cost price, if : $\text{S.P}. = Rs. 1,680$ and profit $=12\%$
Answer$ \text { S.P. }=\text { Rs. } 1,680,$ Profit $=12 \%$
$ \text { C.P. }=\frac{100}{(100+\text { profit })} \times \text { S.P. }$
$ \therefore \text { C.P. }=\frac{100}{(100+12)} \times 1680$
$ =\frac{100 \times 1680}{112}=\frac{25 \times 1680}{28}$
$ =25 \times 60$
$ =\text { Rs. } 1500$
View full question & answer→Question 203 Marks
The selling price of a sofa$-$set is $\frac{4}{5}$ times of its cost price. Find the gain or the loss as a percent.
AnswerLet the cost price $(\text{C.P}.) =1$
$\text { S.P. }=1 \times \frac{4}{5}=\frac{4}{5}$
$ \therefore $Loss$=1-\frac{4}{5}=\frac{5-4}{5}=\frac{1}{5} \ldots .[\because $loss $=\text { C.P. }- \text { S.P. }]$
Loss $\%=\frac{\text { Loss }}{\text { C.P. }}=\frac{\frac{1}{5}}{1} \times 100=\frac{1}{5} \times 100=20 \%$
View full question & answer→Question 213 Marks
By selling a certain number of goods for $Rs. 5,500$; a shopkeeper loses equal to one$-$tenth of their selling price. Find $:(i)$ the loss incurred$(ii)$ the cost price of the goods$(iii)$ the loss as a percent.
Answer$\text { S.P. }=\text { Rs. } 5,500$
Loss $=\frac{1}{10}$ of $(\text{S.P}.) =\frac{1}{10} \times 5500= Rs. 550$
$(i)$ Loss incurred $= Rs. 550$
$(ii) \text{C.P}. = Rs. 5,500+ Rs. 550= Rs. 6,050$
$(iii)$ Loss $\%=\frac{550 \times 100}{6050}=\frac{10 \times 100}{110}=\frac{100}{11}=9 \frac{1}{11} \%$
View full question & answer→Question 223 Marks
Mohit sold a T.V. for $Rs.3,600$; gaining one$-$sixth of its selling price. Find :$(i)$ the gain$(ii)$ the cost price of the T.V.$(iii)$ the gain percent.
Answer$\text{S.P}.$ of T.V. $= Rs. 3,600$
Gain $=\frac{1}{6}$ of $(3600)=\frac{1}{6} \times 3600= Rs. 600$
$(i)$ Thus gain $= Rs. 600$
$(ii)$ Cost price $=3600-600=Rs. 3000$
$(iii)$ Gain $\%=\frac{600}{3000} \times 100=\frac{60}{3}=20 \%$
View full question & answer→Question 233 Marks
An article is bought from Jaipur for Rs. $4,800$ and is sold in Delhi for $Rs. 5,820$. If $Rs.1,200$ is spent on its transportations, etc. ; find he loss or the gain as a percent.
AnswerCost price $=Rs. 4,800$
Selling Price $=Rs. 5,820$
Transport etc. charges $=Rs. 1,200$
Total cost price $= Rs,4,800+Rs.1,200=Rs. 6,000$
Loss $= Rs. 6000 - Rs. 5820 = Rs. 180$
$\therefore$ Loss $\%=\frac{180}{6000} \times 100=3 \%$
View full question & answer→Question 243 Marks
A boy buys an old bicycle for $₹\ 162$ and spends $₹\ 18$ on its repairs before selling the bicycles for $₹$ $207.$ Find his gain or loss percent.
Answerhe buying price of the old bicycle $= ₹ 162$
Money spent on repairs$ = ₹ 18$
Real $\text{C.P}$. of the bicycle $=162+18 = ₹ 180$
$\text{S.P}$. of the bicycle $= ₹ 207$
Profit $= \text{S.P}. – \text{C.P}. = 207 – 180 = ₹ 27$
Gain$\%=\frac{\text { Profit }}{\text { C.P. }} \times 100$
$=\frac{27}{180} \times 100=15 \%$
View full question & answer→Question 253 Marks
The cost price of an article is $30$ percent less than its selling price. Find, the profit or loss as a percent.
AnswerLet $\text{S.P}$. of the article $= Rs\ .100$
$30 \%$ of $\text {S.P.}=Rs \frac{30}{100} \times 100=Rs.30$
$\therefore \text{C.P}$. of the article $=100-30=Rs. 70$
Profit $=\text{S.P}-\text{C.P}$.
$=Rs\ 100- Rs\ 70= Rs \ 30$
Profit $\%=\frac{\text { Profit }}{\text { C.P. }} \times 100$
$=\frac{30}{70} \times 100=\frac{300}{7} \%=42 \frac{6}{7} \%$
View full question & answer→Question 263 Marks
The cost price of an article is $90\%$ of its selling price. What is the profit or the loss as a percent ?
AnswerLet $\text{S.P.}$ of the article $= Rs.100$
$\therefore \text{C.P}$.of the article $=\frac{90}{100} \times 100$
$=Rs. 90$
Gain $= Rs\ 100- Rs\ .90= Rs.\ 10$
Gain $\%=\frac{\text { Gain }}{\text { C.P. }} \times 100$
$=\frac{10}{90} \times 100=\frac{100}{9} \%=11 \frac{1}{9} \%$
View full question & answer→Question 273 Marks
A shopkeeper sells his goods at $80\%$ of their cost price. Find the percent gain or losses?
AnswerLet $\text{C.P}$. of goods $= Rs.100$
$\therefore \text{S.P}$. of goods $=\frac{80}{100} \times 100= Rs. 80$
Loss $=\text{C.P}. - \text{S.P}.$
$= Rs\ 100 -Rs\ . 80 = Rs.\ 20$
Loss $\%=\frac{\text { Loss }}{\text { C.P. }} \times 100$
$=\frac{20}{100} \times 100=20 \%$
View full question & answer→