Class 8 RD Sharma – Chapter 13 Profit Loss Discount And Value Added Tax – Exercise 13.1 | Set 1

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

Solution:

Given, the Cost price of pen = Rs 90

The Selling price of pen = Rs 100

Here, Selling price > Cost price

So, there is a Profit or Gain.

So, Gain = Selling price – Cost price = 100 – 90 = Rs 10

And, Gain % = (Gain/Cost price) × 100 = (10/90) × 100 = 100/9 or 11.12 %

Hence, the gain of a person is Rs 10 and the gain percentage is 100/9 or 11.12 % 

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

Solution:

Given, the Cost price of saree = Rs 1240

The Selling price of saree = Rs 1147

Here, Cost price > Selling price

So, there is a Loss.

So, Loss = Cost price – Selling price = 1240 – 1147 = Rs 93

And, Loss % = (Loss/Cost price) × 100 = (93/1240) × 100 = 7.50%

Hence, Rekha had a loss of Rs 93 and her loss percentage is 7.5 %

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?

Solution:

Given, the Cost price of 9 apples = Rs 9.60

So, the Cost price of 1 apple = Rs 9.60/9 = Rs 1.066

The Selling price of 11 apples = Rs 12

So, the Selling price of 1 apple = Rs 12/11 = Rs 1.090

Here, Selling price > Cost price

So, there is a Profit or Gain.

So, Gain = Selling price – Cost price = 12/11 – 9.60/9 = Rs 0.024

And, Gain % = (Gain/ Cost price) × 100 = (0.024/1.066) × 100 = 2.27 %

Hence, the gain of the boy is Rs 0.024 and the gain percentage is 2.27 % 

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

Solution:

Given, The cost price of 10 articles = the selling price of 9 articles

Let us take x be the Cost price of 1 article

Then, the Cost price of 10 articles will be 10x

So, the Selling price of 9 articles will be 10x 

And, the Selling price of 1 article will be 10x/9

So, we can say Profit or Gain = Selling price – Cost price = 10x/9 – x = x/9

And, Profit % = (Profit/ Cost price) × 100 = (x/9)/x × 100 = 100/9 = 11.11 %

Hence, the profit percentage is 11.11 %

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?

Solution:

Given, the Cost price of radio = Rs 225

Overhead expenses is of Rs 15

So, total Cost price of radio will be Rs 225 + Rs 15 = Rs 240

The Selling price of radio = Rs 300

So, Profit = Selling price – Cost price = 300 – 240 = Rs 60

And, Profit % = (Profit/ Cost price) × 100 = (60/240) × 100 = 25 %

Hence, the profit percentage is 25 %

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?

Solution:

Given, the Cost price of cooler = Rs 1200

Overhead expenses is of Rs 40

So, total Cost price of cooler will be Rs 1200 + Rs 40 = Rs 1240

The Selling price of cooler = Rs 1550

So, Profit = Selling price – Cost price = 1550 – 1240 = Rs 310

And, Profit % = (Profit/ Cost price) × 100 = (310/1240) × 100 = 25 %

Hence, the profit percentage is 25 %

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?

Solution:

Given, the Cost price of wristwatch = Rs 225

Money spent on repairing the watch is Rs 15

So, total Cost price of wristwatch will be Rs 225 + Rs 15 = Rs 240

The Selling price of wristwatch = Rs 300

So, Profit = Selling price – Cost price = 300 – 240 = Rs 60

And, Profit % = (Profit/Cost price) × 100 = (60/240) × 100 = 25 %

Hence, the profit percentage is 25 %

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?

Solution:

Given, Ramesh bought two boxes for Rs 1300

Let us take a be Cost price of 1st box and 1300 – a be Cost price of 2nd box.

Since the first box is sold at a profit of 20%

So, the Selling price of 1st box = a + a × 20/100 = Rs 6a/5

And, the second box is sold at a loss of 12%

So, the Selling price of 2nd box = (1300 – a) – (1300 – a) × 12/100 = Rs (28600 – 22a)/25

It is given that the selling price of both boxes is the same

So, Selling price of 1st box = Selling price of 2nd box

6a/5 = (28600 – 22a)/25

6a/5 = 28600 × 25–22× 25a

So, a = 550

So, the Cost price of 1st box = a = Rs 550

And, the Cost price of 2nd box = 1300 – a = Rs 750

Hence, the Cost price of 1st box is Rs 550 and the Cost price of 2nd box is Rs 750

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

Solution:

Given, The Selling price of 10 pens = the Cost price of 14 pens

Let us take a be the Cost price of 1 pen

Then, the Cost price of 14 pens will be 14a

So, the Selling price of 10 pens will be 14a 

And, the Selling price of 1 pen will be 14a/10

So, we can say Profit or Gain = Selling price – Cost price = 14a/10 – a = 4a/10

And, Gain % = (Gain/ Cost price) × 100 = (4a/10)/a × 100 = 40 %

Hence, the gain percentage is 40 %

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

Solution:

Given, The Cost price of 18 chairs = The Selling price of 16 chairs

Let us take a be the Cost price of 1 chair

Then, the Cost price of 18 chairs will be 18a

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

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

We can clearly see that there is a profit 

So, we can say Profit or Gain = Selling price – Cost price = 18a/16 – a = a/8

And, Gain % = (Gain/ Cost price) × 100 = (a/8)/a × 100 = 12.5 %

Hence, the gain percentage is 12.5 %

Chapter 13 Profit Loss Discount And Value Added Tax – Exercise 13.1 | Set 2