myhelper: RD Sharma solution class 8 chapter 13 Profit ,Discount and Value Added Tax(VAT) Exercise 13.1

Exercise 13.1

Page-13.11

Question 1:

A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain percent.

Answer 1:

$C . P of pen = Rs . 90 S . P of pen = Rs . 100 Gain = SP - CP Gain = 100 - 90 = Rs . 10 Gain % = (\frac{gain \times 100}{C . P .}) = (\frac{10 \times 100}{90}) = 11 \frac{1}{9} %$

Question 2:

Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss percent.

Answer 2:

$C . P of saree = Rs . 1240 S . P of saree = Rs . 1147 Loss = CP - SP Loss = Rs . (1240 - 1147) = Rs . 93 loss % = (\frac{loss \times 100}{C . P .}) = (\frac{93 \times 100}{1240}) = 7.5 %$

Question 3:

A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or loss percent.

Answer 3:

$C . P of 9 apples = Rs 9.60 ∴ C . P of 1 apple = Rs \frac{9.60}{9} = Rs \frac{16}{15} S . P of 11 apples = Rs 12 ∴ S . P of 1 apple = Rs \frac{12}{11} Clearly, S . P of 1 apple > C . P of 1 apple So, we get profit on selling apples Gain % = (\frac{gain \times 100}{C . P .}) = (\frac{\frac{12}{11} - \frac{16}{15}}{\frac{16}{15}}) \times 100 = (\frac{12 \times 15 - 16 \times 11}{15 \times 11}) \times \frac{15}{16} \times 100 = (\frac{180 - 176}{11 \times 16}) \times 100 = (\frac{4}{11 \times 16}) \times 100 = 2 \frac{3}{11} %$

Question 4:

The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.

Answer 4:

$Let the cost price of one article b e Rs . C and t h e selling price be Rs . S T h e r e f o r e, 10 C = 9 S C = \frac{9}{10} S So, t h e cost price is less than t h e selling price . S . P . = (\frac{100 + P rofit %}{100}) C . P S = (\frac{100 + P rofit %}{100}) C \frac{S}{C} = (\frac{100 + P rofit %}{100}) \frac{10}{9} = (\frac{100 + P rofit %}{100}) \frac{1000}{9} = 100 + P rofit % \frac{1000}{9} - 100 = P rofit % P rofit % = \frac{1000 - 900}{9} = 11 \frac{1}{9} Therefore, the required profit percent is 11 \frac{1}{9} % .$

Question 5:

A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the radio for Rs 300, determine his profit percent.

Answer 5:

$Radio costs = Rs . 225 Overhead expenses = Rs . 15 C . P = Rs . (225 + 15) = Rs . 240 S . P = Rs . 300 Profit = SP - CP = Rs . (300 - 240) = Rs . 60 Profit % = \frac{Profit}{C . P} \times 100 = \frac{60}{240} \times 100 = 25 %$

Question 6:

A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he sells the cooler for Rs 1550, determine his profit percent.

Answer 6:

$Cooler costs = Rs . 1200 Overhead expenses = Rs . 40 C . P = Rs . (1200 + 40) = Rs . 1240 S . P = Rs . 1550 Profit = SP - CP = Rs . (1550 - 1240) = Rs . 310 Profit % = \frac{Profit}{C . P} \times 100 = \frac{310}{1240} \times 100 = 25 %$

Question 7:

A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells the same for Rs 300, find his profit percent.

Answer 7:

$A dealer buys a wrist watch f o r Rs . 225 Money spent o n repair i n g t h e w a t c h = Rs . 15 Therefore, C . P = Rs . (225 + 15) = Rs . 240 S . P = Rs . 300 Profit = SP - CP = Rs . (300 - 240) = Rs . 60 Profit % = \frac{Profit}{C . P} \times 100 = \frac{60}{240} \times 100 = 25 %$

Question 8:

Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.

Answer 8:

$Let the cost price of the first box be Rs . x . T h e r e f o r e, t h e \cos t o f t h e s e c o n d b o x w i l l b e Rs . (1300 - x) Profit on the first box = 20 % Loss on the second box = 12 % SP of the first box = CP (\frac{gain % + 100}{100}) SP = x (\frac{120}{100}) S P of the first box = Rs . \frac{120 x}{100} = Rs . \frac{6 x}{5} SP of the second box = CP (\frac{100 - loss %}{100}) S . P of the second box = \frac{88 (1300 - x)}{100} = Rs . (\frac{28600 - 22 x}{25}) Since S . P o f b o t h t h e b o x are equal, \frac{6 x}{5} = (\frac{28600 - 22 x}{25}) 150 x = 143000 - 110 x 260 x = 143000 x = \frac{143000}{260} x = 550 Therefore, t h e cost price of the first box i s Rs . 550 . T h e c ost price of the second box w i l l b e Rs . (1300 - 550) = Rs . 750$

Question 9:

If the selling price of 10 pens is equal to cost price of 14 pens, find the gain percent.

Answer 9:

$Let the cost price of one pen b e Rs . C, a n d t h e s elling price b e Rs . S T h e r e f o r e, 10 S = 14 C C = \frac{10}{14} S However, t h e cost price is less than t h e selling price . S . P . = (\frac{100 + profit %}{100}) C . P S = (\frac{100 + profit %}{100}) C \frac{S}{C} = (\frac{100 + profit %}{100}) \frac{14}{10} = (\frac{100 + profit %}{100}) \frac{1400}{10} = 100 + profit % 140 - 100 = profit % P rofit % = 40 = 40 % Therefore, the required profit percent is 40 % .$

Question 10:

If the cost price of 18 chairs be equal to selling price of 16 chairs, find the gain or loss percent.

Answer 10:

$Let the cost price of one chair b e Rs . C, and selling price be Rs . S T h e r e f o r e, 18 C = 16 S C = \frac{16}{18} S A s cost price is less than t h e selling price, S . P . = (\frac{100 + profit %}{100}) C . P S = (\frac{100 + profit %}{100}) C \frac{S}{C} = (\frac{100 + profit %}{100}) \frac{18}{16} = (\frac{100 + profit %}{100}) \frac{1800}{16} = 100 + profit % \frac{1800}{16} - 100 = profit % P rofit % = \frac{1800 - 1600}{16} = \frac{200}{16} = 12.5 Therefore, the required profit percent is 12.5 % .$

Question 11:

If the selling price of 18 oranges is equal to the cost price of 16 oranges, find the loss percent.

Answer 11:

$Let the cost price of one orange b e Rs . C, and its selling price be Rs . S T h e r e f o r e, 16 C = 18 S C = \frac{18}{16} S A s cost price is more than t h e selling price, S . P . = (\frac{100 - loss %}{100}) C . P S = (\frac{100 - loss %}{100}) C \frac{S}{C} = (\frac{100 - loss %}{100}) \frac{16}{18} = (\frac{100 - loss %}{100}) \frac{1600}{18} = 100 - loss % L oss % = 100 - \frac{1600}{18} L oss % = \frac{1800 - 1600}{18} = \frac{200}{18} = \frac{100}{9} = 11 \frac{1}{9} Therefore, the loss percent is 11 \frac{1}{9} % .$

Question 12:

Ravish sold his motorcycle to Vineet at a loss of 28%. Vineet spent Rs 1680 on its repairs and sold the motor cycle to Rahul for Rs 35910, thereby making a profit of 12.5%, find the cost price of the motor cycle for Ravish.

Answer 12:

$Let the cost price of t h e motorcycle for Ravis h b e Rs . x . Loss % = 28 % Therefore, SP = CP (\frac{100 - Loss %}{100}) SP = Rs . x (\frac{72}{100}) Selling price of the motorcycle for Ravish = Cost price of the motorcycle for Vineet Money spent on repair s = Rs . 1680 T h e r e f o r e, t otal cost price of the motorcycle for Vineet = Rs . (x (\frac{72}{100}) + 1680) Selling price of the motorcycle for Vineet = Rs . 35910 Profit % = 12.5 % SP = CP (\frac{Profit % + 100}{100}) \Rightarrow 35910 = (\frac{72 x}{100} + 1680) (\frac{12.5 + 100}{100}) \Rightarrow 35910 \times 100 \times 100 = (72 x + 168000) (112.5) \Rightarrow 359100000 = 8100 x + 18900000 \Rightarrow 340200000 = 8100 x \Rightarrow x = Rs . 42000 Therefore, Ravis h b o u g h t t h e m o t o r c y c l e f o r Rs . 42000$

Page-13.12

Question 13:

By selling a book for Rs 258, a bookseller gains 20%. For how much should he sell it to gain 30%?

Answer 13:

$Selling price of t h e book = Rs . 258 Gain % = 20 % Since, C . P = [\frac{100}{(100 + Gain %)} \times S . P] = [\frac{100}{(100 + 20)} \times 258] = \frac{25800}{120} = Rs . 215 Let the bookseller s e l l s it f o r Rs . x S o, S . P = [\frac{(100 + Gain %)}{100} \times C . P] x = \frac{100 + 30}{100} \times 215 = \frac{130 \times 215}{100} = Rs . 279.50 Therefore, t h e bookseller must sell t h e b o o k a t Rs 279.50 to m a k e 30 % p r o f i t .$

Question 14:

A defective briefcase costing Rs 800 is being sold at a loss of 8%. If the price is further reduced by 5%, find its selling price.

Answer 14:

$C . P of the briefcase = Rs . 800 Loss = 8 % S . P = CP (\frac{100 - loss %}{100}) = 800 (\frac{100 - 8}{100}) = 800 \times 0.92 = Rs . 736 I f t h e p rice is further reduced by 5 %, t h e s elling price of t h e briefcase w i l l b e = Rs . (736 - 736 \times \frac{5}{100}) = 736 (\frac{100 - 5}{100}) = 736 \times 0.95 = Rs . 699.20 Thus, the selling price of t h e briefcase w i l l b e Rs 699.20 .$

Question 15:

By selling 90 ball pens for Rs 160 a person loses 20%. How many ball pens should be sold for Rs 96 so as to have a profit of 20%?

Answer 15:

$S . P o f 90 b a l l p e n s = Rs . 160 Loss = 20 % Therefore, C . P = SP (\frac{100}{100 - l oss %}) CP = \frac{100}{100 - 20} \times 160 = \frac{16000}{80} = Rs . 200 Now, S . P o f 90 b a l l p e n s = Rs . 96 Profit = 20 % C . P = SP (\frac{100}{100 + Profit %}) CP = \frac{100}{100 + 20} \times 96 = \frac{9600}{120} = Rs . 80 Rs . 200 is the C . P of 90 ball pens . Therefore, Rs . 80 is t h e C . P of = \frac{90 \times 80}{200} = 36 b a l l p e n s Thus, 36 ball pens should be sold a t Rs . 96 to e a r n a profit of 20 % .$

Question 16:

A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.

Answer 16:

$Let the C . P o f t h e a r t i c l e be Rs . x . Original S . P = x + \frac{25}{100} x = R s . \frac{5 x}{4} If he p u r c h a s e d it at 20 % less, C . P = x - \frac{20}{100} x = R s . \frac{4 x}{5} H e s o l d t h e a r t i c l e a t Rs 36.75 less . S o, t h e s e l l i n g p r i c e = R s . \frac{5 x}{4} - 36.75 Given that he would have gained 30 % s e l l i n g a t t h a t p r i c e . T h e r e f o r e, gain % = \frac{S . P - C . P}{C . P} \times 100 S . P - C . P = \frac{5 x}{4} - 36.75 - \frac{4 x}{5} = \frac{5 x}{4} - \frac{4 x}{5} - 36.75 = \frac{25 x - 16 x}{20} - 36.75 = \frac{9 x}{20} - 36.75 So, gain % = \frac{S . P - C . P}{C . P} \times 100 30 = \frac{\frac{9 x}{20} - 36.75}{\frac{4 x}{5}} \times 100 = (\frac{9 x}{20} - 36.75) \times \frac{5}{4 x} \times 100 = \frac{9 x - 735}{16 x} \times 100 30 = \frac{9 x - 735}{16 x} \times 100 \frac{225 x - 18375}{4 x} = 30 225 x - 18375 = 120 x 105 x = 18375 x = \frac{18375}{105} = 175 So, t h e cost price o f t h e a r t i c l e i s Rs . 175 .$

Question 17:

A dishonest shopkeeper professes to sell pulses at his cost price but uses a false weight of 950 gm for each kilogram. Find his gain percent.

Answer 17:

$He sells 950 gm pulses and g e t s a gain o f 50 gm . If he sells 100 gm of pulses, he will gain = \frac{50}{950} \times 100 = \frac{5000}{950} = 5 \frac{5}{19} %$

Question 18:

A dealer bought two tables for Rs 3120. He sold one of them at a loss of 15% and other at a gain of 36%. Then, he found that each table was sold for the same price. Find the cost price of each table.

Answer 18:

$G iven that t h e selling price is same for both the tables . Let t h e C . P of 1 table be Rs . x, then t h e C . P of t h e other w i l l b e Rs . (3120 - x) . Los s o n the first table = 15 % Therefore, S . P = C . P (\frac{100 - l oss %}{100}) S . P = \frac{85 x}{100} = Rs . 0.85 x Gain o n the second table = 36 % Therefore, S . P = C . P (\frac{100 + g ain %}{100}) S . P = Rs . 1.36 (3120 - x) Since both t a b l e s h a v e t h e s a m e S . P, So, 0.85 x = 1.36 (3120 - x) 0.85 x = 4243.20 - 1.36 x 2.21 x = 4243.20 x = \frac{4243.20}{2.21} x = Rs . 1920 So, the cost price of t h e first table i s Rs . 1920 . Cost price of t h e second table = Rs . (3120 - 1920) = Rs . 1200$

Question 19:

Mariam bought two fans for Rs 3605. She sold one at a profit of 15% and the other at a loss of 9%. If Mariam obtained the same amount for each fan, find the cost price of each fan.

Answer 19:

$It is given that t h e S . P is same for both the fans . Let C . P of t h e first fa n b e Rs . x T h e r e f o r e, C . P of t h e second fan = Rs . (3605 - x) Profit o n the first fan = 15 % Loss o n the second fan = 9 % For the first fan, S . P = C . P (\frac{100 + gain %}{100}) = x (\frac{115}{100}) = \frac{23 x}{20} For the second fan, S . P = C . P (\frac{100 - loss %}{100}) = (3605 - x) (\frac{91}{100}) Since S . P o f b o t h t h e f a n s i s t h e same, \frac{23 x}{20} = (3605 - x) (\frac{91}{100}) 2300 x = 91 (72100 - 20 x) 2300 x = 6561100 - 1820 x 4120 x = 6561100 x = Rs . 1592.50 Thus, C . P of t h e first fan i s Rs . 1592.50 . C . P of t h e second fan = Rs . (3605 - 1592.50) = Rs . 2012.50$

Question 20:

Some toffees are bought at the rate of 11 for Rs 10 and the same number at the rate of 9 for Rs 10. If the whole lot is sold at one rupee per toffee, find the gain or loss percent on the whole transaction.

Answer 20:

$Let the t o t a l number of toffees bought b e x . Let \frac{x}{2} toffees at t h e rate of 11 a r e b o u g h t for Rs . 10, a n d \frac{x}{2} toffees at the rate of 9 a r e b o u g h t for Rs . 10 Total money spent on buying t h e toffees = (\frac{x}{2}) (\frac{10}{11}) + (\frac{x}{2}) (\frac{10}{9}) = \frac{200 x}{198} = \frac{100}{99} x It is given that x toffees are sold at one rupee per toffee . Therefore, t h e selling price of x toffees = Rs . x \times 1 = Rs . x As C . P is more than S . P, i t will be a loss . Loss = C . P - S . P = \frac{100}{99} x - x = \frac{100 x - 99 x}{99} = \frac{x}{99} Loss % = \frac{Loss}{C . P} \times 100 \frac{\frac{x}{99}}{\frac{100 x}{99}} \times 100 = 1 % T o t a l loss on the whole transaction would be 1 % .$

Question 21:

A tricycle is sold at a gain of 16%. Had it been sold for Rs 100 more, the gain would have been 20%. Find the C.P. of the tricycle.

Answer 21:

$Let t h e S . P o f t h e t r i c y c l e be Rs . x and C . P be Rs . y Gain % = 16 % S . P = C . P (\frac{100 + gain %}{100}) Then we have, x = y + (\frac{y \times 16}{100}) x = y + 0.16 y x = 1.16 y When S . P increases by Rs . 100, w e g e t \Rightarrow x + 100 = y + (\frac{y \times 20}{100}) Put t i n g x = 1.6 y, w e get \Rightarrow 1.16 y + 100 = y + 0.2 y 1.16 y + 100 = 1.2 y 0.04 y = 100 y = \frac{100}{0.04} = 2500 Thus, C . P of t h e tricycle i s Rs . 2500 .$

Question 22:

Shabana bought 16 dozen ball bens and sold them at a loss equal to S.P. of 8 ball pens. Find
(i) her loss percent
(ii) S.P. of 1 dozen ball pens, if she purchased these 16 dozen ball pens for Rs 576.

Answer 22:

$(i) Number of pens bought = 16 \times 12 = 192 Let the S . P of one pen b e Rs . x . Therefore, S . P of 192 pens = Rs . 192 x S . P of 8 pens = Rs . 8 x It is given that S . P of 8 pens is equal to the loss on selling 192 pens . Therefore, loss = Rs . 8 x C . P of 192 pens = Rs . 576 So, loss = C . P - S . P 8 x = 576 - 192 x 200 x = 576 x = \frac{576}{200} = 2.88 Therefore, loss = 8 (2.88) = Rs . 23.04 Loss % = \frac{loss \times 100}{C . P} = \frac{23.04 \times 100}{576} = 4 % (ii) S . P of 1 pen = Rs . 2.88 Therefore, S . P of 1 dozen pens = 12 x = 12 \times 2.88 = Rs . 34.56$

Question 23:

The difference between two selling prices of a shirt at profits of 4% and 5% is Rs 6. Find
(i) C.P. of the shirt
(ii) the two selling prices of the shirt

Answer 23:

$L et t h e C . P of both the shirts be Rs . x . C . P = Rs . x For shirt 1 : Profit is 4 % : Profit % = \frac{Profit}{CP} \times 100 Profit = \frac{4}{100} \times C . P = Rs . 0.04 x S . P = C . P + Profit = x + 0.04 x = Rs . 1.04 x For shirt 2 : Profit = 5 % : C . P = Rs . x Profit = \frac{5}{100} \times C . P = Rs . 0.05 x S . P = C . P + Profit = x + 0.05 x = Rs . 1.05 x It is given that t h e difference between the i r profit s is Rs . 6 So, 1.05 x - 1.04 x = 6 0.01 x = 6 x = Rs . 600 Thus, C . P = Rs . 600 S . P of shirt 1 = Rs . 1.04 x = Rs . 1.04 \times 600 = Rs . 624 S . P of shirt 2 = Rs . 1.05 x = Rs . 1.05 \times 600 = Rs . 630 .$

Question 24:

Toshiba bought 100 hens for Rs 8000 and sold 20 of these at a gain of 5%. At what gain percent she must sell the remaining hens so as to gain 20% on the whole?

Answer 24:

$C . P of 100 hens = Rs . 8000 Cost of one hen = \frac{8000}{100} = Rs . 80 C . P of 20 hens = Rs . (80 \times 20) = Rs . 1600 Gain % = 5 % S . P = C . P (\frac{100 + g ain %}{100}) S . P = 1600 \times \frac{105}{100} = Rs . 1680 C . P of 80 hens = Rs . (80 \times 80) = Rs . 6400 Gain on 80 hens = S . P of 80 hens - C . P of 80 hens Gain on 100 hens = Gain on 80 hens + Gain on 20 hens Gain on 100 hens = Rs . (80 + S . P of 80 hens - 6400) Gain % on 100 hens = \frac{Gain on 100 hens}{C . P of 100 hens} \times 100 20 = \frac{(80 + S . P of 80 hens - 6400)}{8000} \times 100 1600 = 80 + S . P of 80 hens - 6400 S . P of 80 hens = Rs . (1600 + 6400 - 80) S . P of 80 hens = Rs . 7920 Gain on 80 hens = S . P of 80 hens - C . P of 80 hens = Rs . (7920 - 6400) = Rs . 1520 Gain % on 80 hens = \frac{Gain on 80 hens}{C . P of 80 hens} \times 100 = \frac{1520}{6400} \times 100 = 23.75 % Therefore, T o s h i b a gai n e d 23.75 % o n 80 h e n s .$

RD Sharma solution class 8 chapter 13 Profit ,Discount and Value Added Tax(VAT) Exercise 13.1