# RD Sharma Solutions for Class 8 Chapter 13 Profit, Loss, Discount and Value Added Tax (VAT) Exercise 13.1

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### Access answers to Maths RD Sharma Solutions For Class 8 Exercise 13.1 Chapter 13 Profit, Loss, Discount and Value Added Tax (VAT)

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

Solution:

We know that the cost price of pen = Rs 90

Selling price of pen = Rs 100

By using the formula,

Gain = selling price – cost price

= 100 – 90

= Rs 10

By using the formula,

Gain % = (gain/cost price) × 100

= (10/90) × 100

= 100/9

= (11frac{1}{9}) %

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

Solution:

We know that the cost price of saree = Rs 1240

Selling price of saree = Rs 1147

By using the formula,

Loss = cost price – selling price

= 1240 – 1147

= Rs 93

By using the formula,

Loss % = (loss/cost price) × 100

= (93/1240) × 100

= 7.5 %

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

Solution:

We know that the cost price of 9 apples = Rs 9.60

Cost price of 1 apple = Rs 9.60/9

Selling price of 11 apple = Rs 12

Selling price of 1 apple = Rs 12/11

By using the formula,

Gain = selling price – cost price

= 12/11 – 9.60/9

= (108-105.60)/99

= Rs 2.40/99

By using the formula,

Gain % = (gain/cost price) × 100

= ((2.40/99)/(9.60/9)) × 100

= 25/11

= (2frac{3}{11})%

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

Solution:

We know that the cost price of 10 article = selling price of 9 article

Let us consider CP of 1 article as Rs X

Selling price of 9 article = 10X

Selling price of 1 article = 10x/9

Profit = 10x/9 – x

= x/9

Profit % = Gain % = (gain/cost price) × 100

= (x/9)/x × 100

= 100/9

= (11frac{1}{9})%

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.

Solution:

The cost price of a radio = Rs 225

Total cost = cost price + overhead expenses = 225+15 = Rs 240

Selling price of radio = Rs.300

By using the formula,

Gain = selling price – cost price

= 300 – 240 = Rs 60

By using the formula,

Gain % = (gain/cost price) × 100

= 60/240 × 100

= 25 %

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.

Solution:

We know the cost price of cooler = Rs 1200

Total cost = Rs 1200 + Rs 40 = Rs 1240

Selling price of cooler = Rs 1550

By using the formula,

Gain = selling price – cost price

= Rs 1550 – Rs1240

= Rs 310

By using the formula,

Gain % = (gain/cost price) × 100

= 310/1240 × 100

= 25%

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.

Solution:

We know the cost price of wrist watch = Rs 225

Cost of repairing = Rs 15

Total cost = Rs 225 + Rs 15 = Rs 240

Selling price of watch = Rs 300

By using the formula,

Gain = selling price – cost price

= Rs 300 – Rs 240

= Rs 60

By using the formula,

Gain % = (gain/cost price) × 100

= 60/240 × 100

= 25%

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.

Solution:

We know the cost price of two boxes = Rs 1300

So let us consider cost price of one box be Rs x

Cost price of other box = Rs 1300 – x

Selling price of first box = x + x × 20/100

= x + x/5

= Rs 6x/5

Selling price of second box = (1300 – x) – (1300 – x) × 12/100

= Rs (28600 – 22x)/25

By equating SP of first and second box we get,

6x/5 = (28600 – 22x)/25

150x = 28600 × 5 – 110x

150x + 110x = 28600 × 5

260x = 28600 × 5

x = (28600 × 5)/260

= 550

∴ Cost price of first box = Rs. 550

Cost price of second box = Rs1300 – Rs550 = Rs 750

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

Solution:

Given that, Selling price of 10 pens = cost price of 14 pens

So, let the cost price of 1 pen be Rs x

Selling price of 10 pens = Rs 14x

Selling price of 1 pen =Rs 14x/10

By using the formula,

Gain = selling price – cost price

= 14x/10 – x

= 4x/10

By using the formula,

Gain % = (gain/cost price) × 100

= (4x/10)/x × 100

= 2/5 × 100

= 40%

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

Solution:

Given that, Cost price of 18 chairs = selling price of 16 chairs

So, let the cost price of 1 chair be Rs x

Selling price of 16 chairs =Rs 18x

Selling price of 1 chair = Rs 18x/16

By using the formula,

Gain = selling price – cost price

= 18x/16 – x

= 2x/16

= Rs x/8

By using the formula,

Gain % = (gain/cost price) × 100

= (x/8)/x × 100

= 25/2

= 12 ½ %

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

Solution:

Given that, Selling price of 18 oranges = cost price of 16 oranges

So, let the cost price of 1 orange be Rs x

Selling price of 18 oranges = Rs 16x

Selling price of 1 orange = Rs 16x/18

By using the formula,

Loss = cost price – selling price

= x – 16x/18

= 2x/18

= Rs x/9

By using the formula,

Loss % = (loss/cost price) × 100

= (x/9)/x × 100

= 100/9

= (11frac{1}{9}) %

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.

Solution:

Let us consider the cost price of motorcycle for Ravish be Rs x

Loss% for Ravish = 28%

Selling price for Ravish = x – x × 28/100 = (100x – 28x)/100 = 72x/100

= Rs 18x/25

Selling price for Ravish = cost price for Vineet = Rs 18x/25

Repair cost by Vineet = Rs 1680

Total cost price of the motorcycle for Vineet = Rs18x/25 + Rs 1680

Selling price for Vineet = Rs 35910

Profit = 35910 – (18x+42000)/25

= Rs (855750 – 18x)/25

Profit % = 12.5% (Given)

By using the formula,

Gain % = (gain/cost price) × 100

=> [(855750-18x)/25] / [(18x+42000)/25] × 100 = 12.5

=> [(855750-18x)/25] × [25/(18x+42000)] = 125/1000

=> (855750-18x) / (18x+42000) = 1/8

=> By cross multiplying we get

=> 8(855750-18x) = (18x+42000)

=> 6846000 – 144x = 18x + 42000

=> 6846000 – 42000 = 18x + 144x

=> 162x = 6804000

x = 6804000/162

= 42000

∴ Cost price of motorcycle for Ravish = Rs 42000

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

Solution:

Given details are,

Selling price of book is = Rs 258

The man’s gain percent is = 20% of 100 = 20/100

So, let us consider the cost price of book be Rs x

By solving,

x + x×20/100 = 258

x + x/5 = 258

(5x+x)/5 = 258

By cross multiplying

6x= 5×258

x = 1290/6

= 215

Now, the cost price of book is = Rs 215

For a gain of 30% the man should sell the book at = 215 + 215×30/100

= 215 + 64.5

= 279.50

∴ To gain 30% the man should sell the book at Rs 279.50

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.

Solution:

Given, cost price of the defective briefcase is = Rs. 800

The loss percent is = 8% of 100 = 8/100

Selling price of briefcase is = 800 – 800×8/100

= 800 – 64

= Rs 736

When the price is further reduced by 5% (Given) = 5% of 100 = 5/100

New selling price = 736 – 736×5/100

= 736 – 36.8

= Rs 699.2

∴ The selling price of the defective briefcase is Rs 699.2

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 profit of 20%?

Solution:

Given, selling price for 90 ball pens is = Rs 160

Selling price of 1 ball pen = Rs 160/90 = Rs 16/9

The loss percent is = 20% of 100 = 20/100

Let us consider the cost price of 1 pen be Rs x

By solving,

x – x×20/100 = 16/9

x – x/5 = 16/9

(5x-x)/5 = 16/9

4x/5 = 16/9

By cross multiplying

4x×9 = 16×5

36x = 80

x = 80/36

= Rs 20/9

Now, cost price of 1 ball pen = Rs 20/9

To get a profit of 20%…

Let us consider the number of pens be ‘x’

So, selling price of ‘x’ pens is = Rs 96

Selling price of 1 pen is = Rs 96/x

We know that,

Gain % = (gain/cost price) × 100

20% = [(96/x) – (20/9)] / (20/9) × 100

20/100 = [(96/x) – (20/9)] / (20/9) × 100

(20/100 × 200/9) + 200/90 = 96/x

4/9 + 200/90 = 96/x

(40+200)/90 = 96/x

240/90 = 96/x

24/9 = 96/x

By cross multiplying

24x = 96×9

x = 864/24

= 36

∴ 36 ball pens can be sold at a price of Rs 96

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.

Solution:

Let us consider the cost price of article be Rs x

The Profit percent is = 25% of 100 = 25/100

Selling price of article = x + x × 25/100

= x + x/4

= (4x+x)/4

= Rs 5x/4

If cost price of article is 20% less (given) = 20% of 100 = 20/100

Now, cost price is = x – x×20/100

= x – x/5

= (5x-x)/5

= Rs 4x/5

Now, selling price is = Rs5x/4 – 36.75

The Profit percent is = 30% of 100 = 30/100

He would have gained 30% selling at that price (Given)

We know that, Gain = SP – CP

= 5x/4 – 36.75 – 4x/5

= (25x – 16x)/20 – 36.75

= 9x/20 – 36.75

Gain % = (gain/cost price) × 100

30% = [{(5x/4) – 36.75} – (4x/5)] / (4x/5) × 100

30/100 = (9x/20 – 36.75) / (4x/5) × 100

x = 175

∴ Cost price of article is Rs 175

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.

Solution:

Let us consider the cost price of 1000gm pulses be Rs x

Selling price of 950 gm pulses is also = Rs x

Selling price of 1000 gm pulses = x/950 × 1000

So, Gain = SP – CP

Gain = 1000x/950 – x

= (1000x – 950x)/950

= 50x/950

Gain % = (gain/cost price) × 100

= (50x/950)/x × 100

= 50x/950x × 100

= 5/95 × 100

= 100/19

= (5frac{5}{19})%

∴ The Shopkeeper’s gain percent is (5frac{5}{19})%

18. A dealer bought two tables for Rs 3120. He sold one of them at 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.

Solution:

Given, the cost price of two tables is = Rs 3120

Let cost price of first table be = Rs x

Then, cost price of second table will be = Rs 3120 – x

We know that one is a gain and other is a loss.

Selling price of first table (gain) = x + x × 36/100

= x +9x/25

= (25x + 9x)/25

= Rs 34x/25

Selling price of second table (loss) = (3120 – x) × 85/100

= Rs (3120×85 – 85x)/100

So now, by equating both we get,

34x/25 = (3120×85 – 85x)/100

34x = (3120×85 – 85x)/4

34x × 4 = 3120×85 – 85x

136x + 85x = 3120×85

221x = 3120×85

x = (3120×85)/221

= 1200

∴ Cost price of first table (x) is = Rs 1200

Cost price of second table (3120 – x) = 3120 – 1200 = Rs 1920

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.

Solution:

Given, cost price of 2 fans is = Rs 3605

Let cost price of 1 fan be = Rs x

Then CP of other fan will be = Rs 3605 – x

We know that one is a gain and other is a loss.

Selling price of first fan (gain) = x + x×15/100

= x + x×3/20

= (20x+3x)/20

= Rs 23x/20

Selling price of second fan (loss) = (3605 – x) × 91/100

= Rs (3605×91 – 91x)/100

So now, by equating both we get,

23x/20 = (3605×91 – 91x)/100

23x = (3605×91 – 91x)/5

23x × 5 = 3605×91 – 91x

115x + 91x = 3605×91

206x = 3605×91

x = (3605×91)/206

= 1592.50

∴ Cost price of one fan (x) is = Rs 1592.50

Cost price of second fan (3605 – x) is = 3605 – 1592.50 = Rs 2012.50

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.

Solution:

Let the total number of toffees be ‘x’

Given, cost price of 11 toffees is = Rs 10

Cost price of 1 toffee is = Rs 10/11

Given, cost price of 9 toffees is = Rs 10

Cost price of 1 toffee is = Rs 10/9

When equating both the costs we get,

Cost price of two toffees = (10/11) + (10/9)

= (90 + 110)/99

= 200/99

Cost price of one toffee is = (Rs 200/99)/2 = Rs 200/198

We know that selling price of 1 toffee (Given) = Rs 1

Loss = CP – SP

= 200/198 – 1

= (200-198)/198

= 2/198

Loss% = (loss/cost price) × 100

= (2/198)/(200/198) × 100

= 2/198 × 198/200 × 100

= 2/200 × 100

= 2/2

= 1%

∴ It is 1% loss on the whole truncation.

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.

Solution:

Let us consider the cost price of tricycle be = Rs x

Selling price of the tricycle be = Rs x

Given, Gain% = 16% of 100 = 16/100

Selling price of tricycle = x + x×16/100

= (100x+16x)/100

= 116x/100

= 29x/25

Given, if selling price is Rs 100 more

New Selling price = 29x/25 + 100

Then, Gain% = 20%

By using the formula

Gain % = (gain/cost price) × 100 [by using Gain = SP – CP]

20 = [((29x/25)+100) – x] / x × 100

20x/100 = (29x + 2500 – 25x)/25

x/5 = (29x + 2500 – 25x)/25

5x = 4x + 2500

x = 2500

∴ Cost price of tricycle is Rs 2500

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.

Solution:

Given, number of ball pens bought by Shabana is = 16 dozen = 16×12 = 192 pens

So, let’s consider the cost price of each pen as Rs x

CP of 8 pens = Rs 8x

Let SP of one pen be = Rs x

So, SP of 192 pens = 192x

Given, loss of 192 pens = SP of 8 ball pens

So, loss = 8SP

192x = (192+8) SP

SP = 192x/200

Loss = CP – SP

= x – 192x/200

(i) Loss% = (loss/CP) × 100

= (x – 192x/200)/x × 100

= (200x-192x)/200x × 100

= 8/2

= 4%

(ii) Given, CP of 16 dozen pens = Rs 576

192x = 576

x = 576/192

We know that SP of 1 pen = 192x/200

SP of dozen pens = 12 × 192x/200

= 12 × 192/200 × 576/192

= 12 × 576/200

= 34.56

∴ Loss% = 4% and SP of 1 dozen pens is Rs 34.56

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

Solution:

(i) Let the CP of shirt be = Rs x

Profit (4%) = 4/100 of CP

= 4/100 × x

= 4x/100

Selling Price = C.P + Profit

= x + 4x/100

= (100x + 4x)/100

= 104x/100

(ii) Let the CP of shirt be = Rs x

Profit (5%) = 5/100 of CP

= 5/100 × x

= 5x/100

Selling Price = C.P + Profit

= x + 5x/100

= (100x + 5x)/100

= 105x/100

Given that, the difference between the two selling price is Rs 6

So, 105x/100 – 104x/100 = 6

(105x-104x)/100 = 6

x/100 = 6

x = 600

∴ Now, C.P of the shirt is = Rs 600

Selling Price of one shirt = 104x/100 = (104×600)/100 = Rs 624

Selling Price of other shirt = 105x/100 = (105×600)/100 = Rs 630

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?

Solution:

Given, Total hens = 100

Remaining hens = 100-20 = 80 hens

Toshiba bought 100 hens for = Rs 8000

1 hen cost is = 8000/100 = Rs 80

20hens cost = 20 × 80 = Rs 1600

Given, Gain = 5%

SP = 105/100 × 1600

= Rs 1680

CP for 80 hens = 80 × 80 = Rs 6400

SP of 80 hens = Rs (1600 + 6400-80) = Rs 7920

Gain on 80 hens = SP of 80 hens – CP of 80 hens

= 7920 – 6400

= Rs 1520

Gain % = (gain/cost price) × 100

Gain% on 80 hens = (1520/6400) × 100

= 23.75%

∴ Toshiba require 23.75% gain on the remaining hens (80hens).

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