RD Sharma solution class 8 chapter 13 Profit ,Discount and Value Added Tax(VAT) Exercise 13.2

Exercise 13.2

page-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 1:

(i) We know that SP=MP-DiscountDiscount%=DiscountMP×100Discount=Discount %×MP100=10×1300100So, SP=Rs.1300-10100×1300=1300-130=Rs. 1170(ii) We know that SP=MP- DiscountDiscount %=DiscountMP×100Discount=Discount %×MP100=15×500100So, SP=Rs. 500-15100×500=Rs.(500-75)=Rs. 425

Question 2:

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

Answer 2:

(i) Given, SP=Rs 1222Discount=6%So, MP=100×SP100-Discount%=100×1222100-6=Rs. 1300(ii) Given,SP=Rs. 495 Discount=1%So, MP=100×SP100-Discount%=100×495100-1=Rs. 500

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 3:

(i) We know that SP=MP-DiscountSo, 873=900-DiscountTherefore, Discount=Rs. (900-873)=Rs. 27Discount%=DiscountMP×100%=27900×100%=3%(ii) We know that SP=MP-DiscountSo, 425=500-DiscountTherefore, Discount=Rs.(500-425)=Rs. 75Discount%=DiscountMP×100%=75500×100%=15%

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 4:

Discount = 3%Marked price=Rs. 650Now, 3% of the MP = 3100×650=Rs 19.50So, SP=MP-Discount=650-19.50=Rs 630.50

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 5:

Given, MP of the ceiling fan=Rs. 720 SP of the ceiling fan= Rs. 684Since SP=MP-Discount,Discount=MP-SP=Rs. (720-684)=Rs. 36Discount%=DiscountMP×100%=36720×100%=5%

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 6:

Given,SP of the saree =Rs. 720Discount on the saree=20%We know, Discount%=DiscountMP×100Or, Discount=Discount%×MP100Let the MP of the saree be Rs. xTherefore, Discount=20100x=Rs. 0.02xSince S.P=MP- Discount,720=x-0.20x720=0.80xx=7200.80=Rs. 900Thus, the MP of the saree is Rs. 900.

Question 7:

After allowing a discount of 712% on the marked price, an article is sold for Rs 555. Find its markd price.

Answer 7:

Given,SP of the article=Rs. 555Discount=7.5%Let the MP of the article be Rs. x.Therefore, Discount=Discount×MP100=Rs.7.5x100=Rs. 0.075xSince SP=MP- Discount,555=x-0.075x555=0.925xx=5550.925=Rs. 600Thus, the MP of the article is Rs. 600.

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 8:

Let the CP of the article be Rs. x.MP of the article = Rs. 250Discount=10%Discount= 10% of 250=0.10×250=Rs. 25SP=MP-Discount=250-25=Rs. 225Given,Profit=25%CP=100100+Gain%×SPx=100100+25×225=100125×225=Rs. 180Thus, the CP of the article is Rs. 180.

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 9:

Given,MP of an article=Rs. 500Discount=20%Therefore, Discount=20% of 500=0.20×500=100So, SP=MP-Discount=Rs.(500-100)=Rs. 400CP=100100+Gain%×SP=100100+25×400=40000125=Rs. 320Thus, the actual cost of the article is Rs. 320.

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 10:

Given,CP of the article = Rs. 170Profit = 20%We know that,SP=100+Gain%100×CP=120100×170=20400100=Rs. 204Let the MP of the article be Rs. x.Discount=15%Therefore, Discount=15% of x=0.15xSo, SP=MP-DiscountMP=SP+Discountx=204+0.15xx-0.15x=2040.85x=204x=Rs. 240Thus, the marked price of the article is Rs. 240.

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 11:

Let C.P be Rs x and M.P be Rs y.Gain% = 50We know that,S.P = 100+Gain%100 × C.P= 150100 × x= 32xDiscount% = 25Discount = 25% of y                = Rs 0.25ySo, S.P = M.P - Discount              = y - 0.25y              = 0.75ySo, S.P = 0.75yAlso, S.P = 32xComparing both values for S.P., we get: 32x = 0.75yxy = 0.75 × 23       =1.53        =12Thus, C.P:M.P = 1:2

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 12:

Given, MP of the cycle=Rs. 840 Discount=10%So, SP=MP×100-Discount%100=840×100-10100=Rs. 756Now, SP=Rs. 756 and Gain=26%So, CP=100100+Gain%×756=100126×756=Rs. 600Hence, the actual cost of the cycle is Rs. 600.

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 13:

Let the CP of the item be Rs. x.Profit=10%SP=CP100+Profit%100SP=x110100SP=Rs.1.1xAgain, Profit=SP-CPTherefore, Profit=Rs. (1.1x-x)=Rs. 0.1xWe get,0.1x=56x=Rs. 560Now, the advertised price =1.1x1-0.23=Rs.560×1.10.77=Rs. 800Therefore, the advertised price of the item is Rs. 800.

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 14:

Let the original cost price of the item be Rs. x.MP=x+40x100=1.4xDiscount=MP-SPMP-Discount%×MP100=SP1.4x-5×1.4x100=10641.4x×100-5×1.4x100=1064So, x1.40.95=1064x= 10641.4×0.95=10641.33=Rs. 800Profit=Rs. (1064-800)=Rs. 264Thus, the actual profit by the shopkeeper is Rs. 264.

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 15:

Let the cost price of the pair of earrings be Rs. x.Profit=16%Therefore, SP=Profit%+100100×CP=16+100100x=Rs. 116x100SP-CP=48116x100-x=4816x=4800x=Rs. 300SP=116x100=Rs. 348MP=100×SP100-Discount%=3480075=Rs. 464Thus, CP of the pair of earrings=Rs. x=Rs. 300SP of the pair of earrings=Rs. 348MP of the pair of earrings=Rs. 464

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 16:

Discount allowed by the publisher=32% on the printed pricePrinted price=Rs. 275So, 32% of 275=32100×275=Rs. 88So, the bookseller pays = Rs. 275-Rs. 88=Rs. 187 for a book

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 17:

Let the CP of the lamp be Rs. 100.Loss=10% of CP=Rs. 10So, SP=CP-Loss=Rs. 100-Rs. 10=Rs. 90The trader allows a discount of 20%. This means that when the MP is Rs. 100, the SP will be Rs. 80.Now,If Rs. 80 is the SP, the MP=Rs. 100If Re. 1 is the SP, the M.P=Rs. 10080If Rs. 90 is the SP, the MP=Rs. 10080×90=Rs. 112.50Hence, the trader marks his goods at 12.5% above the cost price.

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 18:

Marked price of the table fan=Rs. 480Discount =25%Therefore, cost price = 25% of Rs. 48025100×480=Rs. 360It is given that the profit on the table fan is 15%.Gain%=GainCP×10015=Gain360×100Gain=Rs. 54Gain=SP-CP54=SP-360SP=Rs. 414Thus, the retailer will sell the table fan for Rs. 414.

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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 19:

Given,SP of the item = Rs. 660Discount on the item = 25%Profit on the item = 10%We know,MP=100×SP100-Discount%=100×660100-25=Rs. 880Thus, the marked price of the item is Rs. 880.

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 20:

Given,Gain on one cycle=Rs. 360Gain=20%Gain%=GainCP×10020=360CP×100CP=Rs. 1800SP=100+Gain%100×CPSP=120100×1800=Rs. 2160SP=Rs. 2160Discount=20%MP=100×SP100-Discount%MP=100×216080=Rs. 2700Hence, the MP of one cycle is Rs. 2700.

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 21:

Given,CP of the suit=Rs. 1470Gain=10%So, SP=Rs. 100+Gain100×CP=Rs. 100+10100×1470=Rs. 1617Now,SP=Rs. 1617Discount=12.5%So, MP=Rs. 100×SP100-Discount%=Rs. 100×1617100-12.5=Rs. 1848Therefore, the marked price of the suit is Rs. 1848.

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 22:

Given,CP of the pair of shoes=Rs. 1470Gain=12% Discount=16%So, SP=Rs. 100+Gain100×CP=Rs. 100+12100×1200=Rs. 1344Now,SP of the pair of shoes=Rs. 1344 Discount=16%So, MP=Rs. 100×SP100-Discount%=Rs. 100×1344100-16=Rs. 1600Aslam should sell the pair of shoes for Rs. 1600.

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 23:

Given, MP of the shirt=Rs. 850Discount=4%Discount allowed=Rs. 4100×850=Rs. 34Thus, SP of the shirt=Rs. 850-34=Rs. 816Now, Profit earned by Jasmine=20%Thus, CP=100×SP100+Profit%=Rs. 100×816100+20=Rs. 100×816120=Rs. 680Thus, the cost price of the shirt is Rs. 680.

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 24:

Given,MP of the pair of shoes=Rs. 1120Discount = 10%So, SP=MP 100-Discount%100=1120×90100=Rs. 1008Now,Profit=26% SP=Rs. 1008Therefore, CP=100×SP100+Profit%Cost price =100×1008100+26=Rs. 800The cost price of the pair of shoes will be Rs. 800.

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 25:

Given,MP of the fan=Rs. 1250Discount=10%So, Discount = 10% of 1250=0.10×1250=Rs. 125Since SP=MP-Discount,SP=Rs. 1250-125=Rs. 1125Now, SP of the fan = Rs. 1125Profit = 25%CP=100100+Profit%×SP=1001251125=Rs. 900Thus, the cost price of the fan is Rs. 900.

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