Question

A dishonest shopkeeper professes to sell grains with only 4% profit, but uses a faulty weight and gives only 800 gm in place of 1 kg. The actual profit percentage of the shopkeeper is:

• A. 24%
• B. 26%
• C. 28%
• D. 30%

Hint:

To calculate the actual profit percentage in such cases, find the difference between the selling price and the cost price for the amount given and divide it by the actual cost price.

Answer 1

The Correct Option is D

Let the cost price of 1 kg be \( C \). The shopkeeper claims to sell 1 kg at a 4% profit. Therefore, the selling price (S.P.) of 1 kg is: \[ S.P. = C + 4% \times C = 1.04C. \] However, the shopkeeper gives only 800 gm instead of 1 kg, so for every 1 kg sold, the shopkeeper actually gives 800 gm, which costs him: \[ \text{Cost Price for 800 gm} = \frac{800}{1000} \times C = 0.8C. \] Thus, his profit on selling 800 gm for the price of 1 kg is: \[ \text{Profit} = S.P. - \text{Cost Price for 800 gm} = 1.04C - 0.8C = 0.24C. \] The actual profit percentage is: \[ \text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price for 800 gm}} \times 100 = \frac{0.24C}{0.8C} \times 100 = 30%. \] Thus, the actual profit percentage is 30%, which corresponds to option (4).