Question

A shopkeeper labelled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labelled price. What is the actual per cent profit earned in the deal?

• A. 18%
• B. 15%
• C. 20%
• D. None of these

Hint:

Assume CP = 100, find the marked price with a 30% markup, then apply the 10% discount to get SP and compute the profit percent.

Answer 1

The Correct Option is D

When a price is marked up by $a\%$ and then discounted by $b\%$, the net percentage change is given by the successive-percentage-change formula:

1. Recall the formula. Net $\% = a - b - \dfrac{ab}{100}$, where $a$ is the markup percent and $b$ is the discount percent.
2. Substitute the values. Here $a = 30$ (markup for profit) and $b = 10$ (discount): $\text{Net} \% = 30 - 10 - \dfrac{30 \times 10}{100} = 30 - 10 - 3 = 17\%$.
3. Interpret the result. A positive net percentage means an overall profit of $17\%$ on the cost price, confirming the direct calculation.

Since $17\%$ does not match 18%, 15% or 20%, the correct choice is option D, "none of these".