RD Sharma Solutions for Class 8 Math 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 Math 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 Book of class 8 Math Chapter 13 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RD Sharma Solutions. All RD Sharma Solutions for class 8 Math 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. 90S.P of pen = Rs. 100Gain=SP -CPGain=100-90=Rs. 10Gain%=gain×100C.P.=10×10090=1119%

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. 1240S.P of saree = Rs. 1147Loss=CP-SPLoss= Rs.(1240-1147)=Rs. 93loss%=loss×100C.P.=93×1001240=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 9.609=Rs1615S.P of 11 apples = Rs 12 S.P of 1 apple=Rs 1211Clearly, S.P of 1 apple >C.P of 1 appleSo, we get profit on selling applesGain%=gain×100C.P.=1211-16151615×100=12×15-16×1115×11×1516×100=180-17611×16×100=411×16×100=2311%

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 be Rs. C and the selling price be Rs. STherefore, 10C=9SC=910SSo, the cost price is less than the selling price.S.P. = 100+Profit%100C.PS=100+Profit%100CSC=100+Profit%100109=100+Profit%10010009=100+Profit%10009-100=Profit%Profit%=1000-9009=1119Therefore, the required profit percent is 1119%.

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. 225Overhead expenses=Rs. 15C.P=Rs. (225+15)=Rs. 240S.P=Rs. 300Profit=SP-CP         = Rs. (300-240)         =Rs. 60Profit%=ProfitC.P×100=60240×100=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.1200Overhead expenses=Rs. 40C.P=Rs. (1200+40)=Rs. 1240S.P=Rs. 1550Profit=SP-CP         =Rs. (1550-1240)         =Rs. 310Profit%=ProfitC.P×100=3101240×100=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 for Rs. 225Money spent on repairing the watch =Rs. 15Therefore,C.P=Rs. (225+15)=Rs. 240S.P=Rs. 300Profit=SP-CP         =Rs. (300-240)         =Rs. 60Profit%=ProfitC.P×100=60240×100=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.Therefore, the cost of the second box will be Rs. (1300-x)Profit on the first box=20 %Loss on the second box=12%SP of the first box=CPgain%+100100SP=x120100SP of the  first box =Rs.120x100=Rs.6x5SP of the second box=CP100-loss%100S.P of the second box=881300-x100=Rs.28600-22x25Since S.P of both the box are equal,6x5=28600-22x25150x=143000-110x260x=143000x=143000260x=550Therefore, the cost price of the first box is Rs. 550.The cost price of the second box will be 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 be Rs. C, and the selling price be Rs. STherefore, 10S=14CC=1014SHowever, the cost price is less than the selling price.S.P. = 100+profit%100C.PS=100+profit%100CSC=100+profit%1001410=100+profit%100140010=100+profit%140-100=profit%Profit%=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 be Rs. C, and selling price be Rs. S Therefore, 18C=16SC=1618SAs cost price is less than the selling price,S.P. = 100+profit%100C.PS=100+profit%100CSC=100+profit%1001816=100+profit%100180016=100+profit%180016-100=profit%Profit%=1800-160016=20016=12.5Therefore, 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 be Rs. C, and its selling price be Rs. STherefore, 16C=18SC=1816SAs cost price is more than the selling price,S.P. = 100-loss%100C.PS=100-loss%100CSC=100-loss%1001618=100-loss%100160018=100-loss%Loss%=100-160018Loss%=1800-160018=20018=1009=1119Therefore, the loss percent is 1119%.

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 the motorcycle for Ravish be Rs. x.Loss%=28%Therefore, SP=CP100-Loss%100SP=Rs. x72100Selling price of the motorcycle for Ravish= Cost  price of the motorcycle for VineetMoney spent on repairs=Rs. 1680Therefore, total cost price of the motorcycle for Vineet=Rs.(  x72100+1680)Selling price of the motorcycle for Vineet =Rs. 35910Profit%=12.5%SP=CPProfit%+10010035910=72x100+168012.5+10010035910×100×100=(72x+168000)(112.5)359100000=8100x+18900000340200000=8100xx=Rs. 42000Therefore, Ravish bought the motorcycle for 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 the book=Rs. 258Gain%=20%Since, C.P = 100100+Gain%×S.P= 100100+20×258=25800120=Rs. 215Let the bookseller sells it for Rs. xSo, S.P = 100+Gain%100×C.Px=100+30100×215=130×215100=Rs. 279.50Therefore, the bookseller must sell the book at Rs 279.50 to make 30% profit.

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. 800Loss=8%S.P =CP 100-loss%100 =800100-8100=800×0.92=Rs. 736If the price is further reduced by 5%, the selling price of the briefcase will be= Rs.736-736×5100 =736100-5100=736×0.95=Rs. 699.20Thus, the selling price of the briefcase will be 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 of 90 ball pens = Rs. 160Loss=20%Therefore, C.P =SP100100-loss%CP=100100-20×160=1600080=Rs. 200Now,S.P of 90 ball pens=Rs. 96Profit=20% C.P =SP100100+Profit%CP=100100+20×96=9600120=Rs. 80Rs. 200 is the C.P of 90 ball pens.Therefore, Rs. 80 is the C.P of =90×80200=36 ball pensThus, 36 ball pens should be sold at Rs. 96 to earn 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 of the article be Rs. x.Original S.P = x+25100x=Rs. 5x4If he purchased it at 20% less,C.P=x-20100x=Rs. 4x5He sold the article at Rs 36.75 less.So, the selling price =Rs. 5x4-36.75Given that he would have gained 30% selling at that price.Therefore, gain%=S.P-C.PC.P×100S.P-C.P=5x4-36.75-4x5=5x4-4x5-36.75=25x-16x20-36.75=9x20-36.75So, gain%=S.P-C.PC.P×10030=9x20-36.754x5×100=9x20-36.75×54x×100=9x-73516x×10030=9x-73516x×100225x-183754x=30225x-18375=120x105x=18375x=18375105=175So, the cost price of the article is 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 950gm pulses and gets a gain of 50gm.If he sells 100gm of pulses, he will gain =50950×100=5000950=5519%

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:

Given that the selling price is same for both the tables.Let the C.P of 1 table be Rs. x, then the C.P of the other will be Rs.3120-x.Loss on the first table= 15%Therefore, S.P=C.P100-loss%100 S.P= 85x100=Rs. 0.85xGain on the second table = 36% Therefore, S.P =C.P100+gain%100S.P=Rs. 1.363120-xSince both tables have the same S.P,So, 0.85x=1.363120-x0.85x=4243.20-1.36x2.21x=4243.20 x =4243.202.21 x=Rs. 1920So,the cost price of the first table is Rs. 1920. Cost price of the 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 the S.P is same for both the fans.Let C.P of the first fan be Rs. xTherefore, C.P of the second fan=Rs. (3605-x)Profit on the first fan=15%Loss on the second fan=9%For the first fan,S.P = C.P100+gain%100=x115100=23x20For the second fan,S.P = C.P 100-loss%100=3605-x91100Since S.P of both the fans is the same,23x20=3605-x911002300x=9172100-20x2300x=6561100-1820x4120x=6561100x=Rs.1592.50Thus, C.P of the first fan is Rs. 1592.50.C.P of the 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 total number of toffees bought be x.Let x2toffees at the rate of 11 are bought for Rs.10, and x2toffees at the rate of 9 are bought for Rs.10Total money spent on buying the toffees= x21011+x2109=200x198=10099xIt is given that x toffees are sold at one rupee per toffee.Therefore, the selling price of x toffees =Rs. x×1=Rs. xAs C.P is more than S.P, it will be a loss.Loss=C.P-S.P=10099x-x=100x-99x99=x99Loss%=LossC.P×100 x99100x99×100=1%Total 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 the S.P of the tricycle be Rs. x and C.P be Rs. y Gain%=16%S.P=C.P100+gain%100Then we have,x=y+y×16100x=y+0.16yx=1.16yWhen S.P increases by Rs. 100, we getx+100=y+y×20100Putting x=1.6y, we get1.16y+100=y+0.2y1.16y+100=1.2y0.04y=100y=1000.04=2500Thus, C.P of the tricycle is 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 =16×12=192Let the S.P of one pen be Rs. x.Therefore, S.P of 192 pens=Rs. 192xS.P of 8 pens=Rs. 8xIt is given that S.P of 8 pens is equal to the loss on selling 192 pens.Therefore, loss= Rs. 8xC.P of 192 pens = Rs. 576So, loss=C.P-S.P8x=576-192x200x=576x=576200=2.88Therefore, loss=82.88=Rs. 23.04Loss%=loss×100C.P=23.04×100576=4%(ii) S.P of 1 pen=Rs. 2.88Therefore, S.P of 1 dozen pens=12x=12×2.88=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:

Let the C.P of both the shirts be Rs. x.C.P=Rs. xFor shirt 1:Profit is 4%:Profit%=ProfitCP×100Profit=4100×C.P= Rs. 0.04xS.P=C.P+Profit=x+0.04x= Rs. 1.04xFor shirt 2:Profit = 5%:C.P= Rs. xProfit=5100×C.P= Rs. 0.05xS.P=C.P+Profit=x+0.05x= Rs. 1.05xIt is given that the difference between their profits is Rs. 6So, 1.05x-1.04x=60.01x=6x= Rs. 600Thus, C.P=Rs. 600S.P of shirt 1=Rs. 1.04x=Rs. 1.04×600=Rs. 624S.P of shirt 2= Rs.1.05x= Rs.1.05×600=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. 8000Cost of one hen=8000100=Rs. 80 C.P of 20 hens =Rs.( 80×20)=Rs. 1600Gain%=5%S.P=C.P100+gain%100S.P=1600×105100=Rs. 1680C.P of 80 hens=Rs.(80×80)=Rs.6400Gain on 80 hens=S.P of 80 hens-C.P of 80 hens Gain on 100 hens =Gain on 80 hens+Gain on 20 hensGain on 100 hens =Rs.(80+S.P of 80 hens - 6400)Gain% on 100 hens=Gain on 100 hensC.P of 100 hens ×10020=(80+S.P of 80 hens - 6400)8000×1001600=80+S.P of 80 hens - 6400S.P of 80 hens=Rs.( 1600+6400-80)S.P of 80 hens=Rs. 7920Gain on 80 hens= S.P of 80 hens -C.P of 80 hens=Rs.(7920-6400)=Rs.1520Gain% on 80 hens =Gain on 80 hensC.P of 80 hens×100=15206400×100=23.75%Therefore, Toshiba gained 23.75% on 80 hens.



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-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

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) 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

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-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%

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:

Discount = 3%Marked price=Rs. 650Now, 3% of the MP = 3100×650=Rs 19.50So, 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. 684Since SP=MP-Discount,Discount=MP-SP=Rs. (720-684)=Rs. 36Discount%=DiscountMP×100%=36720×100%=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. 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.

Page No 13.26:

Question 7:

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

Answer:

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.

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 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.

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. 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.

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:

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.

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% = 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

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:

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.

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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 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.

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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 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.

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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 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

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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 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

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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 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.

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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 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.



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:

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.

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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,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.

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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:

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.

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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:

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.

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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:

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.

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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. 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.

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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. 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.



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 the refrigerator=Rs. 9700VAT=6%So, VAT=6% of Rs. 9700=Rs. 6100×9700=Rs. 582So, the total amount one has 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 of the watch be Rs. x.Then,x+10100x=825x+0.1x=8251.1x=825x=8251.1=Rs. 750Thus, the list price of the watch is Rs. 750.

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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 of the shirt be Rs. x.Then,x+7100x=374.50x+0.07x=374.501.07x=374.50x=374.501.07=Rs. 350Thus, the list price of the shirt is Rs. 350.

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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:

Given,SP of the pair of shoes = Rs. 175VAT=7%Therefore, VAT=7% of Rs. 175=7100×175=Rs. 12.25So, Rani has to pay Rs. 12.25 as VAT.The net value 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:

Given,Amount paid by Swarna for a pair of shoes = Rs. 250VAT paid by her = Rs. 20Let the rate of VAT be x%.Then, x% of 250=20x100×250=202.5x=20x=8Thus, Swarna paid 8% VAT on the pair of shoes.

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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= 5100× 5500= Rs 275 new cost = Rs ( 5500 - 275) = Rs 5225Now,VAT= 5% of 5225=5100× 5225=Rs 261.25 amount to be paid for the goods = Rs ( 5225 + 261.25)= Rs 5486.25

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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. 7150Let the original cost of the furniture be Rs. x.Cost of the furniture=10% of x+x7150=1.10xx=71501.10=Rs. 6500Thus, the original cost of the furniture is Rs. 6500.

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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. 13,750Let the original cost of the furniture be Rs. x.Cost of the furniture=10% of x+x13,750=1.10xx=13,7501.10=Rs. 12,500Thus, the original cost of the furniture is Rs. 12,500.

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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 price of the TV including VAT=Rs. 13440Let the rate of VAT be x%.Cost of the TV=x% of 12000+1200013440-12000=120x120x=1440x=1440120=12Thus, the rate of VAT on the colour TV 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.7x100So, SP of the radio=Rs.x+7x100=Rs.107x100But, SP=Rs. 2568So,107x100=2568x=Rs. 2400Hence, 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:

Given,CP of 2 pair of shoes=Rs. 800×2=Rs. 1600Rate of VAT=5%So, VAT=5% of Rs. 1600=5100×1600=Rs. 80.Therefore, the amount Rajat needs to pay for 2 pair of shoes=Rs. 1600+80=Rs.1680Again,CP of 1 sewing machine=Rs. 1500Rate of VAT=6%So, VAT=6% of Rs. 1500=6100×1500=Rs. 90.Therefore, the amount Rajat needs to pay for 1 sewing machine=Rs. 1500+90=Rs.1590Given,CP of 2 tea-sets=Rs. 650×2=Rs. 1300Rate of VAT=4%So, VAT=4% of Rs. 1300=4100×1300=Rs. 52Therefore, the amount Rajat needs to pay for 2 tea-sets=Rs. 1300+52=Rs. 1352Thus, the total amount Rajat needs 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 + x17600 = 10100 × x + x17600 = 0.10x + x1.10x = 17600x = 176001.10      = 16000Thus, 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. x100×900=Rs. 9xSo,900+9x=9909x=90x=10Thus, Manoj was charged 10% VAT on the leather jacket.

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) Cost of biscuits and bakery products=Rs. 50VAT charged=5%So, VAT=5% of Rs. 50=5100×50=Rs. 2.50So, the total amount paid for biscuits and bakery products=Rs. 50+2.50=Rs. 52.50(ii) Cost of medicine=Rs. 90VAT charged=10%So, VAT=10% of Rs. 90=10100×90=Rs. 9So, the total amount paid for medicines=Rs. 90+9=Rs. 99(iii) Cost of clothes=Rs. 400VAT charged=1%So, VAT=1% of Rs. 400=1100×400=Rs. 4So, the total amount paid for clothes=Rs. 400+4=Rs. 404(iv) Cost of cosmetics=Rs. 150VAT charged=10%So, VAT=10% of Rs. 150=10100×150=Rs. 15So, the total amount paid for cosmetics=Rs. 150+15=Rs. 165Hence, the total amount Rakesh paid at the departmental store=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. xGiven that the VAT charged is 10%.Cost of the set=x+10% of x165=x+0.10x165=1.10xx=1651.10x=Rs. 150Thus, the sale price of the set 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 charged=10%Again, Cost of the bicycle=x+10% of x660=x+0.10x660=1.10xx=6601.10x=Rs. 600Thus, the list price of the 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 charged=8%Given, Cost price of the TV = Rs. 13,500So, Cost price of the TV=x+8% of x13,500=x+0.08x13,500=1.08xx=13,5001.08x=Rs. 12,500Thus, the list price of the 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 of the car=Rs. 2,10,000Discount allowed=5%Therefore, discount=5% of Rs. 2,10,000=5100×2,10,000=Rs. 10,500So, Shikha gets a discount of Rs. 10,500. Therefore, cost of the car will be =Marked price -DiscountRs. ( 2,10,000-10,500)=Rs. 1,99,500VAT=10% of 1,99,500=10100×199500=Rs. 19,950Thus, the amount 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 the cosmetic items be Rs. x and the price of the purse be Rs. y.VAT=15% of x=15x100=Rs. 3x20VAT=10% of y=10y100=Rs. y10So, SP of cosmetic items=x+3x20=Rs. 23x20SP of purse=y+y10=Rs. 11y10But the selling price of the cosmetic items and the purse is Rs. 345 and Rs. 110 respectively.So,23x20=345x=Rs. 300and11y10=11011y=1100y=Rs. 100Total price=Rs. (300+100)=Rs. 400Now,Let the VAT on the whole transaction be r%.r% of 400=r100×400=4rTotal transaction=Rs. 345+110=Rs. 455So,4r+400=4554r=55r=554=13.75Thus, VAT charged on the 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 of the cooler, excluding VAT, be Rs. x.VAT=10% of Rs x=10100×x=Rs. x10Therefore, SP of the cooler will be=Rs. x+x10=Rs. 11x10But the SP is already given as Rs. 2563.So, 2563=11x1011x=25630x=2563011=Rs. 2330Hence, discount allowed 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 of the washing machine=Rs. 9000Discount allowed=5%Discount=5% of Rs. 9000=5100×9000=Rs. 450So, the cost of the washing machine=List price-Discount=Rs. (9000-450)=Rs. 8550VAT=10% of Rs. 8550=10100×8550=Rs. 855Thus, the customer has to pay=Rs. 8550+855=Rs. 9405



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