Class 8 RD Sharma – Chapter 13 Profit Loss Discount And Value Added Tax – Exercise 13.1 | Set 2

Chapter 13 Profit Loss Discount And Value Added Tax – Exercise 13.1 | Set 1

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

Solution: 

Given, The Selling price of 18 oranges = the Cost price of 16 oranges

Let us take a as the Cost price of 1 orange

Then, the Cost price of 16 oranges will be 16a

So, the Selling price of 18 oranges will be 16a 

And, the Selling price of 1 orange will be 16a/18

We can clearly see that there is a loss

And Loss = Cost price – Selling price = a – 16a/18 = a/9

And, Loss % = (Loss/Cost price) × 100 = (a/9)/a × 100 = 11.11%

Hence, the loss percentage is 11.11%

Question 12. Ravish sold his motorcycle to Vineet at a loss of 28%. Vineet spent Rs 1680 on its repairs and sold the motorcycle to Rahul for Rs 35910, thereby making a profit of 12.5%, find the cost price of the motorcycle for Ravish?

Solution:

Let a be the cost price of the motorcycle for Ravish

Given, loss % of Ravish = 28 %

So, we can conclude the Selling price of motorcycle for Ravish = a – a × 28/100 = Rs 18a/25

We know, the selling price for Ravish = The cost price for Vineet = Rs 18a/25

Also, money spend on repairing by Vineet = Rs 1680

So, the total cost price of the motorcycle for Vineet = Rs 18a/25 + Rs 1680 = Rs (18a + 42000)/25

The selling price of the motorcycle for Vineet = Rs 35910 [Given]

We can say, Profit = Selling price – Cost price

= 35910 – (18a + 42000)/25

= Rs (855750 – 18a)/25

Also, the profit % = 12.5 % [Given]

We know the formula of profit % = (profit/cost price) × 100

12.5 = [(855750 – 18a)/25] / [(18a + 42000)/25] × 100

a = 42000

Hence, the cost price of the motorcycle for Ravish is Rs 42000

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

Solution:

Given, the Selling price of the book = Rs 258

The Gain % = 20 %

So, we can say that Cost price of book = (Selling price × 100)/(100 + Gain %) = (258 × 100)/(100 + 20) = Rs 215

Now we have to find the selling price to have a 30 % profit percentage,

So, applying the formula 

Selling price of book = [Cost price × (100 + Gain %)]/100 = [215 × (100 + 30)]/100 = Rs 279.50

Hence, the person should sell the book for Rs 279.50 in order to have a 30 % profit percentage.

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?

Solution:

Given, the Cost price of a briefcase = Rs 800

Loss % = 8 %

So, Selling price of briefcase = [Cost price × (100 – Loss %)]/100 = [800 × (100 – 8)]/100 = Rs 736

Now, the 5 % reduction in the selling price of a briefcase,

So, new Selling price = 736 – (736 × 5)/100 = Rs 699.2

Hence, the selling price of the defective briefcase is Rs 699.2

Question 15. By selling 90 ball pens for Rs 160 a person loses 20%. How many ball pens should be sold for Rs 96 to have a profit of 20%?

Solution: 

Given, the Selling price of 90 ball pens is Rs 160

So, we can say the selling price of 1 ball pen = Rs 160/90 = Rs 16/9 

Also, the loss % = 20 %

So, the Cost price of 1 pen can be derived as 

Cost price = (Selling price × 100)/(100 – loss%) = (16 × 100)/9 × (100 – 20) = Rs 20/9

Now for second case, profit % = 20%

And Selling price can be derived as 

Selling price = Cost price × (100 + profit %)/100 = 20 × (100 + 20)/ 9 × 100 = Rs 8/3

So, we can say with Rs 8/3 we can buy 1 ball pen 

And, with Rs 1 we can buy 3/8 pen

With Rs 96 we can buy (3 × 96)/8 pens = 36 pens

Hence, 36 ball pens would be sold for Rs 96 to have a profit of 20%

Question 16. A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article?

Solution:

Let Rs 100 be the Cost price of the article 

Also, for the first case profit % is 5 %

So, the Selling price will be Rs 100 + 25 = Rs 125

For the second case, 

The Cost price will be 20% less than Rs 100 i.e Rs 80

Here profit % is 30 %

So, the Selling price can be derived as 

S.P = C.P × (100 + profit%)/100 = 80 × (100 + 30)/100 = Rs 104

So the difference in the Selling price in both cases is Rs 125 – Rs 104 = Rs 21

If Rs 21 is less, the Cost price is Rs 100

If Rs 1 is less, the Cost price is Rs 100/21

And if Rs 36.75 is less, the Cost price is Rs (100 × 36.75)/21 = Rs 175

Hence, the cost price of the article is Rs 175

Question 17. A dishonest shopkeeper professes to sell pulses at his cost price but uses a false weight of 950 gm for each kilogram. Find his gain percent?

Solution:

Let a be the Cost price of 1000gm/1kg pulses

And as per the question, the Selling price of 950 gm pulses is also Rs a

So, the Selling price of 1000 gm pulses will be (a/950) × 1000

The gain will be Selling price – Cost price 

i.e 1000a/950 – a = 50a/950

And the Gain % = (Gain/Cost price) × 100 = (50a/950)/a × 100 = 5.26 %

Hence, the gain percentage of the shopkeeper is 5.26 %

Question 18. A dealer bought two tables for Rs 3120. He sold one of them at a loss of 15% and others at a gain of 36%. Then, he found that each table was sold at the same price. Find the cost price of each table?

Solution:

Given, the Cost price of 2 tables is Rs 3120

Let Rs 100 be the Selling price of each table

For Table 1, 

The loss% is 15 %

So, Cost price = (Selling price × 100)/(100 – loss%) = (100 × 100)/(100 – 15) = Rs 10000/85

For Table 2,

The profit% is 36 %

So, Cost price = (Selling price × 100)/(100 + profit%) = (100 × 100)/(100 + 36) = Rs 10000/136

Ratios between two tables = 10000/85 : 10000/136 = 136 : 85

The sum of ratio’s of tables = 136 + 85 = 221

Also, the total Cost price of tables = 3120

So, the Cost price of Table 1 can be derived as Rs (3120 × 136)/221 = Rs 1920

And, the Cost price of Table 2 can be derived as Rs (3120 × 85)/221 = Rs 1200

Hence, the cost price of tables one and two is Rs 1920 and Rs 1200 respectively.

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?

Solution:

Given, the Cost price of 2 fans is Rs 3605

Let Rs 100 be the Selling price of each fan

For Fan1, 

The profit% is 15 %

So, Cost price = (Selling price × 100)/(100 + profit%) = (100 × 100)/(100 + 15) = Rs 10000/115

For Fan 2,

The loss% is 9 %

So, Cost price = (Selling price × 100)/(100 – loss%) = (100 × 100)/(100 – 9) = Rs 10000/91

Ratios between two fans = 10000/115 : 10000/91 = 115 : 91

The sum of ratio’s of fans = 115 + 91 = 206

Also, the total Cost price of fans = 3605

So, the Cost price of Fan 1 can be derived as Rs (3605 × 115)/206 = Rs 2012.50

And, the Cost price of Fan 2 can be derived as Rs (3605 × 91)/206 = Rs 1592.50

Hence, the cost price of fan one and two is Rs 2012.50 and Rs 1592.50 respectively.

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?

Solution:

Given, the Cost price of 11 toffees is Rs 10

So, the cost price of 1 will be Rs 10/11

Also, the Cost price of 9 toffees is Rs 10

So, the cost price of 1 will be Rs 10/9

So, we get the cost price of both toffees = (10/11) + (10/9) = 200/99

So, we can derive that the cost price of 1 toffee will be (Rs 200/99)/2 = Rs 200/198

Also, the selling price of 1 toffee is Rs 1 [Given]

We can say there is a loss, loss = Cost price – Selling price = 200/198 – 1 = 2/198

And, the loss% = (loss/cost price) × 100 = (2/198)/(200/198) × 100 = 1 %

Hence, there is a loss percentage of 1 % in the whole transaction

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?

Solution:

Let Rs 100 be the cost price of the tricycle

For the first case, there is gain% of 16%

So, the selling price will be Rs 100 + 16 = Rs 116

For the first case, there is gain% of 20%

So, the selling price will be Rs 100 + 20 = Rs 120

The difference in selling prices = Rs 120 – Rs 116 = Rs 4

If the difference is Rs 4, the cost price is Rs 100

If the difference is Rs 1, the cost price is Rs 100/4

And, If the difference is Rs 100, the cost price is Rs (100/4) × 100 = Rs 2500

Hence, the cost price of the given tricycle is Rs 2500

Question 22. Shabana bought 16 dozen ball pens 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:

i) Given, the number of pens bought = 16 dozens = 16 × 12 = 196 pens

Let a be the selling price of one pen

So, the selling price of 12 pens will be 192a

Also, the cost price of 8 pens is 8a

Given, the selling price of 8 pens will be equal to lose on selling 192 pens

So, we can say that loss will be 8a

The cost price of 192 pens is Rs 576

The Loss will be Cost price – Selling price

So, 8a = 576 – 192a

a = 2.88

So, the loss = 8a = 8 × 2.88 = Rs 23.04

And, the loss% = (loss/cost price) × 100 = 4 %

Hence, the loss is Rs 23.04 and the loss percentage is 4%

ii) The selling price of one pen is Rs 2.88 as derived above

So, the Selling price of 1 dozen pens will be 12 × 2.88 = Rs 34.56

Hence, the selling price of 1 dozen pens is Rs 34.56

Question 23. The difference between the 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:

Given, the difference between the two selling prices of shirts = Rs 6

Also, the difference in their profit percentages = 5% – 4% = 1%

i) The Cost price of the shirt will be derived as (difference in selling price × difference in profit % × 100) = 1 × 6 × 100 = 600 

Hence, the Cost price of the shirt is Rs 600

ii) And, the Selling price can be derived as 

The selling price of the first shirt = Cost price × (100 + profit%)/100 

= 600 × (100 + 4)/100 = Rs 624

The selling price of the second shirt = Cost price × (100 + profit%)/100 

= 600 × (100 + 5)/100 = Rs 630

Hence, the selling price of the first and second shirt is Rs 624 and Rs 630 respectively

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?

Solution:

Given, the number of Hens is 100

The remaining number of hens is 100 – 20 = 80

Toshiba buy 100 hens for Rs 8000

So, the cost of 1 hen is Rs 8000/100 = Rs 80

And, the cost price of 20 hens will be Rs 20 × 80 = Rs 1600

Also, there is a gain% of 5%

The selling price can be (105/100) × 1600 = Rs 1680

We can say the cost price of 80 hens = 80 × 80 = Rs 6400

And the selling price of 80 hens = Rs (1600 + 6400 – 80) = Rs 7920

The gain will be Cost price – Selling price = 7920 – 6400 = Rs 1520

The gain% = (gain/cost price) × 100

= (1520/6400) × 100

= 23.75%

Hence, Toshiba must sell the remaining hens on the profit percentage of  23.75%