Rd Sharma 2019 2020 for Class 8 Maths Chapter 13 - Proft, Loss, Discount And Value Added Tax Vat

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Rd Sharma 2019 2020 Solutions for Class 8 Maths Chapter 13 Proft, Loss, Discount And Value Added Tax Vat are provided here with simple step-by-step explanations. These solutions for Proft, Loss, Discount And Value Added Tax Vat are extremely popular among Class 8 students for Maths Proft, Loss, Discount And Value Added Tax Vat Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2019 2020 Book of Class 8 Maths Chapter 13 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2019 2020 Solutions. All Rd Sharma 2019 2020 Solutions for class Class 8 Maths are prepared by experts and are 100% accurate.

Page No 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:

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

Page No 13.11:

Question 2:

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

Answer:

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

Page No 13.11:

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:

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

Page No 13.11:

Question 4:

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

Answer:

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

Page No 13.11:

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:

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

Page No 13.11:

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:

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

Page No 13.11:

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:

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

Page No 13.11:

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:

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

Page No 13.11:

Question 9:

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

Answer:

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

Page No 13.11:

Question 10:

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

Answer:

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

Page No 13.11:

Question 11:

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

Answer:

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

Page No 13.11:

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:

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

Page No 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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.12:

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:

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

Page No 13.26:

Question 1:

Find the S.P. if
(i) M.P. = Rs 1300 and Discount = 10%
(ii) M.P. = Rs 500 and Discount = 15%

Answer:

$(i) We know that SP = MP - D iscount Discount % = \frac{Discount}{MP} \times 100 Discount = \frac{Discount % \times MP}{100} = \frac{10 \times 1300}{100} So, SP = Rs . (1300 - (\frac{10}{100} \times 1300)) = 1300 - 130 = Rs . 1170 (ii) We know that SP = MP - D iscount Discount % = \frac{Discount}{MP} \times 100 Discount = \frac{Discount % \times MP}{100} = \frac{15 \times 500}{100} So, SP = Rs . (500 - (\frac{15}{100} \times 500)) = Rs . (500 - 75) = Rs . 425$

Page No 13.26:

Question 2:

Find the M.P. if
(i) S.P. = Rs 1222 and Discount = 6%
(ii) S.P. = Rs 495 and Discount = 1%

Answer:

$(i) G i v e n, SP = Rs 1222 Discoun t = 6 % So, MP = (\frac{100 \times SP}{100 - Discount %}) = \frac{100 \times 1222}{100 - 6} = Rs . 1300 (ii) G i v e n, SP = Rs . 495 Discount = 1 % So, MP = (\frac{100 \times SP}{100 - Discount %}) = \frac{100 \times 495}{100 - 1} = Rs . 500$

Page No 13.26:

Question 3:

Find discount in percent when
(i) M.P. = Rs 900 and S.P. = Rs 873
(ii) M.P. = Rs 500 and S.P. = Rs 425

Answer:

$(i) We know that SP = MP - D iscount So, 873 = 900 - D iscount T h e r e f o r e, Discount = Rs . (900 - 873) = Rs . 27 Discount % = \frac{Discount}{MP} \times 100 % = \frac{27}{900} \times 100 % = 3 % (ii) We know that SP = MP - D iscount So, 425 = 500 - D iscount T h e r e f o r e, Discount = Rs . (500 - 425) = Rs . 75 Discount % = \frac{Discount}{MP} \times 100 % = \frac{75}{500} \times 100 % = 15 %$

Page No 13.26:

Question 4:

A shop selling sewing machines offers 3% discount on all cash purchases. What cash amount does a customer pay for a sewing machine the price of which is marked as Rs 650.

Answer:

$D iscount = 3 % Marked price = Rs . 650 Now, 3 % of the MP = \frac{3}{100} \times 650 = Rs 19.50 S o, SP = MP - Discount = 650 - 19.50 = Rs 630.50$

Page No 13.26:

Question 5:

The marked price of a ceiling fan is Rs 720. During off season, it is sold for Rs 684. Determine the discount percent.

Answer:

$Given, MP of the ceiling fan = Rs . 720 SP of the ceiling fan = Rs . 684 Since SP = MP - Discount, Discount = MP - SP = Rs . (720 - 684) = Rs . 36 Discount % = (\frac{Discount}{MP}) \times 100 % = \frac{36}{720} \times 100 % = 5 %$

Page No 13.26:

Question 6:

On the eve of Gandhi Jayanti a saree is sold for Rs 720 after allowing 20% discount. What is its marked price?

Answer:

$Given, SP of the saree = Rs . 720 Discount o n t h e s a r e e = 20 % W e k n o w, Discount % = \frac{Discount}{MP} \times 100 O r, Discount = \frac{Discount % \times MP}{100} Let t h e MP o f t h e s a r e e be Rs . x T h e r e f o r e, Discount = \frac{20}{100} x = Rs . 0.02 x Since S . P = MP - D iscount, 720 = x - 0.20 x 720 = 0.80 x x = \frac{720}{0.80} = Rs . 900 Thus, t h e MP o f t h e s a r e e is Rs . 900 .$

Page No 13.26:

Question 7:

After allowing a discount of $7 \frac{1}{2} %$ on the marked price, an article is sold for Rs 555. Find its markd price.

Answer:

$Given, SP o f t h e a r t i c l e = Rs . 555 Discount = 7.5 % Let t h e MP o f t h e a r t i c l e b e Rs . x . T h e r e f o r e, Discount = \frac{Discount \times MP}{100} = Rs . \frac{7.5 x}{100} = Rs . 0.075 x Since SP = MP - D iscount, 555 = x - 0.075 x 555 = 0.925 x x = \frac{555}{0.925} = R s . 600 Thus, t h e MP o f t h e a r t i c l e is Rs . 600 .$

Page No 13.26:

Question 8:

A shopkeeper allows his customers 10% off on the marked price of goods and still gets a profit of 25%. What is the actual cost to him of an article marked Rs 250?

Answer:

$Let t h e CP o f t h e a r t i c l e be Rs . x . MP of the article = Rs . 250 Discount = 10 % Discount = 10 % of 250 = 0.10 \times 250 = Rs . 25 SP = MP - D iscount = 250 - 25 = Rs . 225 Given, P rofit = 25 % CP = [\frac{100}{(100 + Gain %)} \times SP] x = [\frac{100}{(100 + 25)} \times 225] = [\frac{100}{125} \times 225] = R s . 180 Thus, t h e CP o f t h e a r t i c l e is Rs . 180 .$

Page No 13.26:

Question 9:

A shopkeeper allows 20% off on the marked price of goods and still gets a profit of 25%. What is the actual cost to him of an article marked Rs 500?

Answer:

$Given, MP of an article = Rs . 500 Discount = 20 % T h e r e f o r e, Discount = 20 % of 500 = 0.20 \times 500 = 100 So, SP = MP - Discount = Rs . (500 - 100) = Rs . 400 CP = [\frac{100}{(100 + Gain %)} \times SP] = [\frac{100}{(100 + 25)} \times 400] = \frac{40000}{125} = R s . 320 Thus, t h e actual cost o f t h e a r t i c l e is Rs . 320 .$

Page No 13.26:

Question 10:

A tradesman marks his goods at such a price that after allowing a discount of 15%, he makes a profit of 20%. What is the marked price of an article whose cost price is Rs 170?

Answer:

$G i v e n, C P o f t h e a r t i c l e = R s . 170 P r o f i t = 20 % We know that, SP = [\frac{(100 + Gain %)}{100} \times CP] = [\frac{120}{100} \times 170] = \frac{20400}{100} = Rs . 204 Let t h e MP o f t h e a r t i c l e be Rs . x . Discount = 15 % T h e r e f o r e, Discount = 15 % of x = 0.15 x So, SP = MP - Discount MP = SP + Discount x = 204 + 0.15 x x - 0.15 x = 204 0.85 x = 204 x = Rs . 240 Thus, the marked p rice o f t h e a r t i c l e is Rs . 240 .$

Page No 13.26:

Question 11:

A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked price, he still makes a profit of 50%. Find the ratio of the C.P. to the M.P.

Answer:

$Let C . P be Rs x and M . P be Rs y . Gain% = 50 We know that, S . P = [\frac{(100 + Gain %)}{100} \times C . P] = [\frac{150}{100} \times x] = \frac{3}{2} x Discount % = 25 Discount = 25 % of y = Rs 0.25 y So, S . P = M . P - Discount = y - 0.25 y = 0.75 y So, S . P = 0.75 y Also, S . P = \frac{3}{2} x Comparing both values for S.P., we get: \frac{3}{2} x = 0.75 y \frac{x}{y} = \frac{0.75 \times 2}{3} = \frac{1.5}{3} = \frac{1}{2} Thus, C . P : M . P = 1 : 2$

Page No 13.26:

Question 12:

A cycle dealer offers a discount of 10% and still makes a profit of 26%. What is the actual cost to him of a cycle whose marked price is Rs 840?

Answer:

$G i v e n, MP of the cycle = Rs . 840 Discount = 10 % So, SP = MP \times (\frac{100 - Discount %}{100}) = 840 \times (\frac{100 - 10}{100}) = Rs . 756 Now, SP = Rs . 756 and Gain = 26 % So, CP = \frac{100}{100 + Gain %} \times 756 = \frac{100}{126} \times 756 = Rs . 600 Hence, the actual cost o f t h e c y c l e is Rs . 600 .$

Page No 13.26:

Question 13:

A shopkeeper allows 23% commision on his advertised price and still makes a profit of 10%. If he gains Rs 56 on one item, find his advertised price.

Answer:

$Let t h e CP o f t h e i t e m be Rs . x . Profit = 10 % SP = CP (\frac{100 + Profit %}{100}) SP = x (\frac{110}{100}) SP = Rs . 1.1 x A g a i n, Profit = SP - CP T h e r e f o r e, Profit = Rs . (1.1 x - x) = Rs . 0.1 x We get, 0.1 x = 56 x = Rs . 560 Now, t h e advertise d price = \frac{1.1 x}{1 - 0.23} = Rs . \frac{560 \times 1.1}{0.77} = Rs . 800 T h e r e f o r e, t h e a d v e r t i s e d p r i c e o f t h e i t e m i s R s . 800 .$

Page No 13.26:

Question 14:

A shopkeeper marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers. What actual profit does he make, if he receives Rs 1064 after paying the discount?

Answer:

$Let the original cost price o f t h e i t e m be Rs . x . MP = x + \frac{40 x}{100} = 1.4 x Discount = M P - S P MP - \frac{Discount % \times MP}{100} = SP 1.4 x - \frac{5 \times 1.4 x}{100} = 1064 \frac{1.4 x \times 100 - 5 \times 1.4 x}{100} = 1064 So, x (1.4) (0.95) = 1064 x = \frac{1064}{(1.4 \times 0.95)} = \frac{1064}{1.33} = Rs . 800 Profit = Rs . (1064 - 800) = Rs . 264 Thus, t h e actual profit b y t h e s h o p k e e p e r is Rs . 264 .$

Page No 13.26:

Question 15:

By selling a pair of earings at a discount of 25% on the marked price, a jeweller makes a profit of 16%. If the profit is Rs 48, what is the cost price? What is the marked price and the price at which the pair was eventually bought?

Answer:

$Let the cost price o f t h e p a i r o f e a r r i n g s be Rs . x . Profit = 16 % T h e r e f o r e, SP = (\frac{Profit % + 100}{100}) \times CP = (\frac{16 + 100}{100}) x = R s . \frac{116 x}{100} SP - CP = 48 \Rightarrow \frac{116 x}{100} - x = 48 \Rightarrow 16 x = 4800 \Rightarrow x = Rs . 300 SP = \frac{116 x}{100} = Rs . 348 MP = \frac{100 \times SP}{100 - Discount %} = \frac{34800}{75} = Rs . 464 Thus, CP o f t h e p a i r o f e a r r i n g s = Rs . x = Rs . 300 SP o f t h e p a i r o f e a r r i n g s = Rs . 348 MP o f t h e p a i r o f e a r r i n g s = Rs . 464$

Page No 13.26:

Question 16:

A publisher gives 32% discount on the printed price of a book to booksellers. What does a bookseller pay for a book whose printed price is Rs 275?

Answer:

$Discount a l l o w e d b y t h e p u b l i s h e r = 32 % on t h e printed price Printed price = Rs . 275 So, 32 % of 275 = \frac{32}{100} \times 275 = Rs . 88 So, t h e bookseller pay s = Rs . 275 - Rs . 88 = Rs . 187 f o r a b o o k$

Page No 13.26:

Question 17:

After allowing a discount of 20% on the marked price of a lamp, a trader loses 10%. By what percentage is the marked price above the cost price?

Answer:

$Let the CP o f t h e l a m p b e Rs . 100 . Loss = 10 % of CP = Rs . 10 So, SP = CP - L oss = Rs . 100 - Rs . 10 = Rs . 90 The trader allows a discount of 20 % . This means that when t h e MP is Rs . 100, the SP will be Rs . 80 . Now, If Rs . 80 is the SP, th e MP = Rs . 100 If Re . 1 is the SP, the M . P = Rs . \frac{100}{80} If R s . 90 is the SP, the MP = Rs . (\frac{100}{80} \times 90) = Rs . 112.50 Hence, the trader mark s his good s a t 12.5 % above the cost price .$

Page No 13.26:

Question 18:

The list price of a table fan is Rs 480 and it is available to a retailer at 25% discount. For how much should a retailer sell it to gain 15%?

Answer:

$Marked price o f t h e t a b l e f a n = Rs . 480 Discount = 25 % Therefore, cost price = 25 % of R s . 480 \frac{25}{100} \times 480 = Rs . 360 It is given that t h e p r o f i t o n t h e t a b l e f a n i s 15 % . Gain % = \frac{Gain}{CP} \times 100 15 = \frac{Gain}{360} \times 100 Gain = Rs . 54 Gain = SP - CP 54 = SP - 360 SP = Rs . 414 T h u s, t h e r e t a i l e r w i l l s e l l t h e t a b l e f a n f o r R s . 414 .$

Page No 13.27:

Question 19:

Rohit buys an item at 25% discount on the marked price. He sells it for Rs 660, making a profit of 10%. What is the marked price of the item?

Answer:

$G i v e n, S P o f t h e i t e m = R s . 660 D i s c o u n t o n t h e i t e m = 25 % P r o f i t o n t h e i t e m = 10 % We know, MP = (\frac{100 \times SP}{100 - Discount %}) = (\frac{100 \times 660}{100 - 25}) = Rs . 880 Thus, the marked price o f t h e i t e m is Rs . 880 .$

Page No 13.27:

Question 20:

A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs 360 over the sale of one cycle, find the marked price of the cycle.

Answer:

$Given, G a i n o n o n e c y c l e = Rs . 360 Gain = 20 % Gain % = \frac{Gain}{CP} \times 100 20 = \frac{360}{CP} \times 100 CP = Rs . 1800 SP = \frac{100 + Gain %}{100} \times CP SP = \frac{120}{100} \times 1800 = Rs . 2160 SP = Rs . 2160 Discount = 20 % MP = \frac{100 \times SP}{100 - Discount %} MP = \frac{100 \times 2160}{80} = Rs . 2700 Hence, t h e M P o f o n e c y c l e i s Rs . 2700 .$

Page No 13.27:

Question 21:

Jyoti and Meena run a ready-made garment shop. They mark the garments at such a price that even after allowing a discount of 12.5%, they make a profit of 10%. Find the marked price of a suit which costs them Rs 1470.

Answer:

$G i v e n, C P of the suit = Rs . 1470 Gain = 10 % So, SP = Rs . (\frac{100 + Gain}{100} \times CP) = Rs . (\frac{100 + 10}{100} \times 1470) = Rs . 1617 Now, SP = Rs . 1617 D iscount = 12.5 % So, MP = Rs . (\frac{100 \times SP}{100 - Discount %}) = Rs . (\frac{100 \times 1617}{100 - 12.5}) = Rs . 1848 T h e r e f o r e, t h e m a r k e d p r i c e o f t h e s u i t i s R s . 1848 .$

Page No 13.27:

Question 22:

What price should Aslam mark on a pair of shoes which costs him Rs 1200 so as to gain 12% after allowing a discount of 16%?

Answer:

$G i v e n, CP of the pair of shoes = Rs . 1470 Gain = 12 % Discount = 16 % So, SP = Rs . (\frac{100 + Gain}{100} \times CP) = Rs . (\frac{100 + 12}{100} \times 1200) = Rs . 1344 Now, SP of the pair of shoes = Rs . 1344 D iscount = 16 % So, MP = Rs . (\frac{100 \times SP}{100 - Discount %}) = Rs . (\frac{100 \times 1344}{100 - 16}) = Rs . 1600 A s l a m s h o u l d s e l l t h e p a i r o f s h o e s f o r R s . 1600 .$

Page No 13.27:

Question 23:

Jasmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt for her marked at Rs 850?

Answer:

$G i v e n, MP of the shirt = Rs . 850 Discount = 4 % Discount allowed = Rs . (\frac{4}{100} \times 850) = Rs . 34 Thus, SP of t h e shirt = Rs . (850 - 34) = Rs . 816 Now, P rofi t e a r n e d b y Jasmine = 20 % Thus, CP = \frac{100 \times SP}{(100 + Profit %)} = Rs . (\frac{100 \times 816}{100 + 20}) = Rs . (\frac{100 \times 816}{120}) = Rs . 680 Thus, the cost price of t h e shirt is Rs . 680 .$

Page No 13.27:

Question 24:

A shopkeeper offers 10% off-season discount to the customers and still makes a profit of 26%. What is the cost price for the shopkeeper on a pair of shoes marked at Rs 1120?

Answer:

$Given, MP of the pair of shoes = Rs . 1120 D i s c o u n t = 10 % So, SP = MP (\frac{100 - Discount %}{100}) = 1120 \times \frac{90}{100} = Rs . 1008 Now, P r o f i t = 26 % SP = Rs . 1008 Therefore, CP = (\frac{100 \times SP}{100 + P r o f i t %}) Cost price = (\frac{100 \times 1008}{100 + 26}) = Rs . 800 T h e \cos t p r i c e o f t h e p a i r o f s h o e s w i l l b e R s . 800 .$

Page No 13.27:

Question 25:

A lady shopkeeper allows her customers 10% discount on the marked price of the goods and still gets a profit of 25%. What is the cost price of a fan for her marked at Rs 1250?

Answer:

$Given, MP of the fan = Rs . 1250 Discount = 10 % So, Discount = 10 % of 1250 = 0.10 \times 1250 = Rs . 125 Since SP = MP - Discount, S P = Rs . (1250 - 125) = Rs . 1125 N o w, S P o f t h e f a n = R s . 1125 P r o f i t = 25 % CP = [\frac{100}{(100 + P r o f i t %)} \times SP] = [\frac{100}{125}] 1125 = Rs . 900 Thus, t h e \cos t p r i c e o f t h e f a n i s Rs . 900 .$

Page No 13.32:

Question 1:

The list price of a refrigerator is Rs 9700. If a value added tax of 6% is to be charged on it, how much one has to pay to buy the refrigerator?

Answer:

$List price of t h e refrigerator = Rs . 9700 VAT = 6 % So, VAT = 6 % of Rs . 9700 = Rs . \frac{6}{100} \times 9700 = Rs . 582 So, t h e total amount o n e h a s to pay = Rs . 9700 + Rs . 582 = Rs . 10, 282$

Page No 13.32:

Question 2:

Vikram bought a watch for Rs 825. If this amount includes 10% VAT on the list price, what was the list price of the watch?

Answer:

$Let the list price o f t h e w a t c h be Rs . x . Then, x + \frac{10}{100} x = 825 x + 0.1 x = 825 1.1 x = 825 x = \frac{825}{1.1} = R s . 750 Thus, t h e list price o f t h e w a t c h is Rs . 750 .$

Page No 13.32:

Question 3:

Aman bought a shirt for Rs 374.50 which includes 7% VAT. Find the list price of the shirt.

Answer:

$Let the list price o f t h e s h i r t be Rs . x . Then, x + \frac{7}{100} x = 374.50 x + 0.07 x = 374.50 1.07 x = 374.50 x = \frac{374.50}{1.07} = R s . 350 Thus, t h e list price o f t h e s h i r t is Rs . 350 .$

Page No 13.32:

Question 4:

Rani purchases a pair of shoes whose sale price is Rs 175. If she pays VAT at the rate of 7%, how much amount does she poy as VAT? Also, find the net value of the pair of shoes.

Answer:

$G i v e n, S P o f t h e p a i r o f s h o e s = R s . 175 VAT = 7 % T h e r e f o r e, VAT = 7 % of Rs . 175 = \frac{7}{100} \times 175 = Rs . 12.25 So, R a n i h a s to pay Rs . 12.25 as VAT . T h e n e t v a l u e of the pair of shoes = Rs . 175 + Rs . 12.25 = Rs . 187.25$

Page No 13.32:

Question 5:

Swarna paid Rs 20 as VAT on a pair of shoes worth Rs 250. Find the rate of VAT.

Answer:

$G i v e n, A m o u n t p a i d b y S w a r n a f o r a p a i r o f s h o e s = R s . 250 V A T p a i d b y h e r = R s . 20 Let the rate of VAT be x % . Then, x % of 250 = 20 \frac{x}{100} \times 250 = 20 2.5 x = 20 x = 8 Thus, S w a r n a p a i d 8 % V A T o n t h e p a i r o f s h o e s .$

Page No 13.32:

Question 6:

Sarita buys goods worth Rs 5500. She gets a rebate of 5% on it. After getting the rebate if VAT at the rate of 5% is charged, find the amount she will have to pay for the goods.

Answer:

$Price after getting a rebate of 5 % on Rs 5500 = 5 % of 5500 = \frac{5}{100} \times 5500 = Rs 275 ∴ new cost = Rs (5500 - 275) = Rs 5225 Now, VAT = 5 % of 5225 = \frac{5}{100} \times 5225 = Rs 261.25 ∴ a mount to be paid for the goods = Rs (5225 + 261.25) = Rs 5486.25$

Page No 13.32:

Question 7:

The cost of furniture inclusive of VAT is Rs 7150. If the rate of VAT is 10%, find the original cost of the furniture.

Answer:

$Cost of the furniture inclusive VAT = Rs . 7150 Let the original cost of the furniture be Rs . x . Cost of the furniture = 10 % of x + x 7150 = 1.10 x x = \frac{7150}{1.10} = Rs . 6500 Thus, the original cost of the furniture is Rs . 6500 .$

Page No 13.32:

Question 8:

A refrigerator is available for Rs 13750 including VAT. If the rate of VAT is 10%, find the original cost of the furniture.

Answer:

$Cost of the refrigerator inclusive VAT = Rs . 13, 750 Let the original cost of the furniture be Rs . x . Cost of the furniture = 10 % of x + x 13, 750 = 1.10 x x = \frac{13, 750}{1.10} = Rs . 12, 500 Thus, the original cost of the furniture is Rs . 12, 500 .$

Page No 13.32:

Question 9:

A colour TV is available for Rs 13440 inclusive of VAT. If the original cost of TV is Rs 12000, find the rate of VAT.

Answer:

$Cost p r i c e of the TV inclu d i n g VAT = Rs . 13440 Let the rate of VAT be x % . Cost of the TV = x % of 12000 + 12000 13440 - 12000 = 120 x 120 x = 1440 x = \frac{1440}{120} = 12 Thus, the rate of VAT o n t h e c o l o u r T V is 12 % .$

Page No 13.32:

Question 10:

Reena goes to a shop to buy a radio, costing Rs 2568. The rate of VAT is 7%. She tells the shopkeeper to reduce the price of the radio such that she has to pay Rs 2568, inclusive of VAT. Find the reduction needed in the price of radio.

Answer:

$Let the reduced price, excluding VAT, of the radio be Rs x . Then, VAT = 7 % of Rs . x = Rs . \frac{7 x}{100} So, SP of the radio = Rs . (x + \frac{7 x}{100}) = Rs . \frac{107 x}{100} But, SP = Rs . 2568 So, \frac{107 x}{100} = 2568 x = Rs . 2400 Hence, the reduction needed in the price of the radio = Rs . (2568 - 2400) = Rs . 168 .$

Page No 13.32:

Question 11:

Rajat goes to a departmental store and buys the following articles:

Item	Price per item	Rate of VAT
2 Pairs of shoes 1Sewing machine 2 Tea-sets	Rs 800 Rs 1500 Rs 650	5% 6% 4%

Calculate the total amount he has to pay to the store.

Answer:

$G i v e n, CP of 2 pair of shoes = Rs . 800 \times 2 = Rs . 1600 Rate of VAT = 5 % So, VAT = 5 % of Rs . 1600 = \frac{5}{100} \times 1600 = Rs . 80 . T h e r e f o r e, t h e amount R a j a t n e e d s t o pa y for 2 pair of shoes = Rs . (1600 + 80) = Rs . 1680 A g a i n, CP of 1 sewing machine = Rs . 1500 Rate of VAT = 6 % So, VAT = 6 % of Rs . 1500 = \frac{6}{100} \times 1500 = Rs . 90 . T h e r e f o r e, t h e amount R a j a t n e e d s t o pa y for 1 sewing machine = Rs . (1500 + 90) = Rs . 1590 G i v e n, CP of 2 t e a - sets = Rs . 650 \times 2 = Rs . 1300 Rate of VAT = 4 % So, VAT = 4 % of Rs . 1300 = \frac{4}{100} \times 1300 = Rs . 52 T h e r e f o r e, t h e amount R a j a t n e e d s t o pa y for 2 t ea - sets = Rs . (1300 + 52) = Rs . 1352 Thus, t h e total amount R a j a t n e e d s to pay = Rs . (1680 + 1590 + 1352) = Rs . 4622$

Page No 13.33:

Question 12:

Ajit buys a motorcycle for Rs 17600 including value added tax. If the rate of VAT is 10%, what is the sale price of the motorcycle?

Answer:

$Let the sale price of the motorcycle be Rs x . Cost including VAT = 10 % of x + x 17600 = \frac{10}{100} \times x + x 17600 = 0.10 x + x 1.10 x = 17600 x = \frac{17600}{1.10} = 16000 Thu s, the sale price of the motorcycle is Rs 16000 .$

Page No 13.33:

Question 13:

Manoj buys a lather coat costing Rs 900 at Rs 990 after paying the VAT. Calculate the rate of VAT charge on the coat.

Answer:

$Let the rate of VAT be x % . Then, VAT = Rs . (\frac{x}{100} \times 900) = Rs . 9 x S o, 900 + 9 x = 990 9 x = 90 x = 10 Thus, M a n o j w a s c h a r g e d 10 % VAT o n t h e l e a t h e r j a c k e t .$

Page No 13.33:

Question 14:

Rakesh goes to a departmental store and purchases the following articles:
(i) biscuits and bakery products costing Rs 50, VAT @ 5%,
(ii) medicines costing Rs 90, VAT @ 10%,
(iii) clothes costing Rs 400, VAT @ 1%, and
(iv) cosmetics costing Rs 150, VAT @ 10%.
Calculate the total amount to be paid by Rakesh to the store.

Answer:

$(i) C o s t o f b iscuits and bakery products = Rs . 50 VAT c h a r g e d = 5 % So, VAT = 5 % of Rs . 50 = \frac{5}{100} \times 50 = Rs . 2.50 So, t h e t o t a l amount paid for biscuits and bakery products = Rs . (50 + 2.50) = Rs . 52.50 (ii) C ost o f m e d i c i n e = Rs . 90 VAT c h a r g e d = 10 % So, VAT = 10 % of Rs . 90 = \frac{10}{100} \times 90 = Rs . 9 So, t h e t o t a l amount paid for medicines = Rs . (90 + 9) = Rs . 99 (iii) C ost o f c l o t h e s = Rs . 400 VAT c h a r g e d = 1 % So, VAT = 1 % of Rs . 400 = \frac{1}{100} \times 400 = Rs . 4 So, t h e t o t a l amount paid for clothes = Rs . (400 + 4) = Rs . 404 (iv) C ost o f \cos m e t i c s = Rs . 150 VAT c h a r g e d = 10 % So, VAT = 10 % of Rs . 150 = \frac{10}{100} \times 150 = Rs . 15 So, t h e t o t a l amount paid for cosmetics = Rs . (150 + 15) = Rs . 165 Hence, t h e total amount Rakesh p a i d a t t h e d e p a r t m e n t a l s t o r e = Rs . (52.50 + 99 + 404 + 165) = Rs . 720.50$

Page No 13.33:

Question 15:

Rajeeta purchased a set of cosmetics. She paid Rs 165 for it including VAT. If the rate of VAT is 10%, find the sale price of the set.

Answer:

$Let the sale price of the set be Rs . x G i v e n t h a t t h e VA T c h a r g e d i s 10 % . Cost o f t h e s e t = x + 10 % of x 165 = x + 0.10 x 165 = 1.10 x x = \frac{165}{1.10} x = R s . 150 Thus, t h e s a l e p r i c e o f t h e s e t is Rs . 150 .$

Page No 13.33:

Question 16:

Sunita purchases a bicycle for Rs 660. She has paid a VAT of 10%. Find the list price of the bicycle?

Answer:

$Let the sale price of the bicycle be Rs . x . VAT c h a r g e d = 10 % A g a i n, Cost o f t h e b i c y c l e = x + 10 % of x 660 = x + 0.10 x 660 = 1.10 x x = \frac{660}{1.10} x = R s . 600 Thus, t h e list p r i c e o f t h e bicycle is Rs . 600 .$

Page No 13.33:

Question 17:

The sales price of a television, inclusive of VAT, is Rs 13,500. If VAT charged at the rate of 8% of the list price, find the list price of the television.

Answer:

$Let the list price of the TV be Rs . x . VAT c h a r g e d = 8 % G i v e n, C o s t p r i c e o f t h e T V = R s . 13, 500 S o, Cost p r i c e o f t h e T V = x + 8 % of x 13, 500 = x + 0.08 x 13, 500 = 1.08 x x = \frac{13, 500}{1.08} x = R s . 12, 500 Thus, t h e list p r i c e o f t h e TV is Rs . 12, 500 .$

Page No 13.33:

Question 18:

Shikha purchased a car with a marked price of RS 210000 at a discount of 5%. If VAT is charged at the rate of 10%, find the amount Shikha had paid for purchasing the car.

Answer:

$Marked price o f t h e c a r = Rs . 2, 10, 000 D iscount a l l o w e d = 5 % T h e r e f o r e, d i s c o u n t = 5 % of Rs . 2, 10, 000 = \frac{5}{100} \times 2, 10, 000 = Rs . 10, 500 S o, S hikha get s a d i s c o u n t o f Rs . 10, 500 . T h e r e f o r e, c ost of t h e car will be = Marked price - D iscount Rs . (2, 10, 000 - 10, 500) = Rs . 1, 99, 500 VA T = 10 % of 1, 99, 500 = \frac{10}{100} \times 199500 = Rs . 19, 950 Thus, t h e a mount paid by Shikha to purchase the car = Rs . (1, 99, 500 + 19, 950) = Rs . 2, 19, 450$

Page No 13.33:

Question 19:

Shruti bought a set of cosmetic items for Rs 345 including 15% value added tax and a purse for Rs 110 including 10% VAT. What percent is the VAT charged on the whole transaction?

Answer:

$Let the price of t h e cosmetic items be R s . x and t h e p rice of t h e purse be Rs . y . VAT = 15 % of x = \frac{15 x}{100} = R s . \frac{3 x}{20} VAT = 10 % of y = \frac{10 y}{100} = R s . \frac{y}{10} So, SP of cosmetic items = x + \frac{3 x}{20} = R s . \frac{23 x}{20} SP of purse = (y + \frac{y}{10}) = R s . \frac{11 y}{10} But t h e selling price of t h e cosmetic i t e m s and t h e purse i s Rs . 345 and Rs . 110 r e s p e c t i v e l y . So, \frac{23 x}{20} = 345 x = R s . 300 and \frac{11 y}{10} = 110 11 y = 1100 y = R s . 100 Total price = Rs . (300 + 100) = Rs . 400 N o w, L e t t h e VAT on the whole transaction be r % . r % of 400 = \frac{r}{100} \times 400 = 4 r T otal transaction = R s . 345 + 110 = R s . 455 So, 4 r + 400 = 455 4 r = 55 r = \frac{55}{4} = 13.75 Thus, VAT c h a r g e d on t h e whole transaction is 13.75 % .$

Page No 13.33:

Question 20:

List price of a cooler is Rs 2563. The rate of VAT is 10%. The customer requests the shopkeeper to allow a discount in the price of the cooler to such an extent that the price remains Rs 2563 inclusive of VAT. Find the descount in the price of the cooler.

Answer:

$Let the reduced price o f t h e c o o l e r, excluding VAT, be Rs . x . VAT = 10 % of Rs x = \frac{10}{100} \times x = R s . \frac{x}{10} T h e r e f o r e, SP of the cooler will be = Rs . (x + \frac{x}{10}) = Rs . \frac{11 x}{10} But t h e SP i s a l r e a d y given a s Rs . 2563 . So, 2563 = \frac{11 x}{10} 11 x = 25630 x = \frac{25630}{11} = Rs . 2330 Hence, d iscount a l l o w e d in the price of the cooler = Rs . (2563 - 2330) = Rs . 233 .$

Page No 13.33:

Question 21:

List price of a washing machine is Rs 9000. If the dealer allows a discount of 5% on the cash payment, how much money will a customer pay to the dealer in cash, if the rate of VAT is 10%?

Answer:

$List price o f t h e w a s h i n g m a c h i n e = Rs . 9000 Discount a l l o w e d = 5 % Discount = 5 % of Rs . 9000 = \frac{5}{100} \times 9000 = Rs . 450 So, t h e c ost of the washing machine = List price - D iscount = Rs . (9000 - 450) = Rs . 8550 VAT = 10 % of Rs . 8550 = \frac{10}{100} \times 8550 = Rs . 855 Thus, t h e customer has to pay = Rs . (8550 + 855) = Rs . 9405$

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