The percentage profit earned by selling an article for Rs.2,100 is equal to the percentage loss incurred by selling the same article for Rs.1,460. At what price should the article be sold to make 20% profit?

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 21 Jun, 2024 Shift 1)

Answer 1

Given:

The percentage profit earned by selling an article for Rs. 2,100 is equal to the percentage loss incurred by selling the same article for Rs. 1,460.

Formula Used:

Let the cost price (CP) of the article be Rs. x.

Profit percentage = Loss percentage

Profit = Selling Price (SP) - Cost Price (CP)

Loss = Cost Price (CP) - Selling Price (SP)

Calculation:

Let the cost price (CP) be Rs. x.

Profit earned by selling at Rs. 2,100:

Profit = 2,100 - x

Loss incurred by selling at Rs. 1,460:

Loss = x - 1,460

Since the profit percentage is equal to the loss percentage:

(2,100 - x) / x × 100 = (x - 1,460) / x × 100

⇒ 2,100 - x = x - 1,460

⇒ 2,100 + 1,460 = 2x

⇒ 3,560 = 2x

⇒ x = 1,780

To make a 20% profit, the selling price (SP) should be:

SP = CP + 20% of CP

SP = 1,780 + 20% of 1,780

SP = 1,780 + 0.20 × 1,780

SP = 1,780 + 356

SP = 2,136

The article should be sold at Rs. 2,136 to make a 20% profit.