The percentage profit earned by selling an article for ₹3,471 is equal to the percentage loss incurred by selling the same article for ₹2,577. At what price should the article be sold (in ₹) to make a 25% profit?​

Correct option is B

Given:

Selling Price 1 (SP₁) = ₹3,471

Selling Price 2 (SP₂) = ₹2,577

The percentage profit on SP₁ is equal to the percentage loss on SP₂;

Required: Selling price to earn 25% profit.

Concept Used:

When profit% = loss% on the same article, the Cost Price (CP) is the average of the two selling prices.

This follows from:

​$$\frac{SP₁ - CP}{CP} \times 100 = \frac{CP - SP₂}{CP} \times 100$$​​

SP₁ - CP = CP - SP₂ 

2CP = SP₁ + SP₂

CP = $$\frac{SP₁ + SP₂}{2}$$​​

Formula Used:

SP = $$CP \times \left(1 + \frac{Profit\%}{100} \right)$$​​

Solution:

CP = $$\frac{3471 + 2577}{2} = \frac{6048}{2}$$​  = ₹3024

To make a 25% profit:

SP = $$3024 \times \left(1 + \frac{25}{100}\right) = 3024 \times 1.25$$ = ₹3780