A bought an article and spent Rs.410 on its repairs. He then sold it to B at a profit of 30%. B sold it to C at a loss of 20%. C finally sold it for Rs.2288 at a profit of 10%. How much did A pay for the article? (In Rs.)

Given:

Repair cost for A = ₹ 410

Profit of A = 30%

Loss of B = 20%

Selling price of C = ₹ 2288

Profit of C = 10%

Formula Used:

Selling Price = Cost Price × (1 + Profit Percentage/100)

Selling Price = Cost Price × (1 - Loss Percentage/100)

Calculations:

Let the cost price for C be CP_C.

Selling price for C = CP_C × (1 + 10/100)

⇒ 2288 = CP_C × 1.1

⇒ CP_C = 2288 / 1.1 = 2080

The cost price for C is the selling price for B. Let the cost price for B be CP_B.

Selling price for B = CP_B × (1 - 20/100)

⇒ 2080 = CP_B × 0.8

⇒ CP_B = 2080 / 0.8 = 2600

The cost price for B is the selling price for A. Let the cost price for A be CP_A.

Selling price for A = (CP_A + 410) × (1 + 30/100)

⇒ 2600 = (CP_A + 410) × 1.3

⇒ (CP_A + 410) = 2600 / 1.3 = 2000

⇒ CP_A = 2000 - 410 = 1590

∴ The correct answer is Option (1).