Question

A shopkeeper sells an item with a loss of 5%. If he had sold it for Rs 120 more, he would have gained 15%. Find the cost price of the item.

• A. Rs 550
• B. Rs 600
• C. Rs 580
• D. Rs 520

Hint:

In profit and loss problems, use the formula \( \text{Selling Price} = \text{Cost Price} \pm \text{Percentage} \).

Answer 1

The Correct Option is B

Let the cost price be \( C \). The selling price with a 5% loss is: \[ \text{Selling Price with loss} = C - 0.05C = 0.95C \] The selling price with a 15% gain is: \[ \text{Selling Price with gain} = C + 0.15C = 1.15C \] The difference between the selling prices is Rs 120: \[ 1.15C - 0.95C = 120 \] \[ 0.20C = 120 \] \[ C = \frac{120}{0.20} = 600 \] Thus, the cost price of the item is Rs 600.