When the article sold at the rate of Rs.10464 earned a profit of 18% more than that of the loss incurred when the same article was sold at the rate of Rs.5232. Find the cost price of the article. (In Rs.)

Given:

Selling Price 1 (SP₁) = ₹10,464 (Profit incurred)

Selling Price 2 (SP₂) = ₹5,232 (Loss incurred)

Profit earned = Loss incurred + 18% of Loss incurred

Formula used:

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

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

Calculation:

Let the Cost Price of the article be CP.

Profit (P) = SP₁ - CP = 10464 - CP

Loss (L) = CP - SP₂ = CP - 5232

Profit = Loss + 18% of Loss

⇒ Profit = Loss × \((1 + \dfrac{18}{100})\)

⇒ Profit = Loss × (1 + 0.18)

⇒ Profit = Loss × 1.18

Substitute the expressions for Profit and Loss into the equation:

(10464 - CP) = (CP - 5232) × 1.18

⇒ 10464 - CP = 1.18 × CP - (1.18 × 5232)

⇒ 10464 - CP = 1.18 CP - 6173.76

⇒ 10464 + 6173.76 = 1.18 CP + CP

⇒ 16637.76 = 2.18 CP

⇒ CP = \(\dfrac{16637.76}{2.18}\)

⇒ CP = 7632

∴ The cost price of the article is ₹7,632.