Question

A sells an item at a loss of 10%. If he had sold it for ₹ 120 more, he would have gained 5%. What is the cost price of the item?

• A. ₹ 680
• B. ₹ 720
• C. ₹ 800
• D. ₹ 850

Hint:

To solve problems involving profit and loss, set up equations for the selling price based on the percentage gain or loss and use the given conditions to solve for the cost price.

Answer 1

The Correct Option is C

Let the cost price of the item be \( C \). - Selling at a loss of 10% means that the selling price \( SP_1 \) is: \[ SP_1 = C \times \left(1 - \frac{10}{100}\right) = C \times 0.90 \] - If the item was sold for ₹120 more, the new selling price \( SP_2 \) would be: \[ SP_2 = SP_1 + 120 = C \times 0.90 + 120 \] - Selling at a gain of 5% means that the new selling price \( SP_2 \) is also: \[ SP_2 = C \times \left(1 + \frac{5}{100}\right) = C \times 1.05 \] Now, equating the two expressions for \( SP_2 \): \[ C \times 0.90 + 120 = C \times 1.05 \] Solving for \( C \): \[ 120 = C \times 1.05 - C \times 0.90 \] \[ 120 = C \times (1.05 - 0.90) \] \[ 120 = C \times 0.15 \] \[ C = \frac{120}{0.15} = 800 \] Thus, the cost price of the item is ₹800.