Question

Two numbers A and B are less than a third number C by 15% and 32%, respectively. By what percent (%) is number B less than the number A?

• A. 32
• B. 26
• C. 17
• D. 20

Hint:

To find the percentage difference between two numbers, first find the difference, then divide by the reference number and multiply by 100.

Answer 1

The Correct Option is D

Let the number \( C \) be the reference number. Then, \[ A = C \times \left( 1 - \frac{15}{100} \right) = C \times 0.85 \] and \[ B = C \times \left( 1 - \frac{32}{100} \right) = C \times 0.68 \] We are asked to find the percentage by which \( B \) is less than \( A \). The difference between \( A \) and \( B \) is: \[ A - B = C \times 0.85 - C \times 0.68 = C \times (0.85 - 0.68) = C \times 0.17 \] The percentage by which \( B \) is less than \( A \) is: \[ \frac{A - B}{A} \times 100 = \frac{C \times 0.17}{C \times 0.85} \times 100 = \frac{0.17}{0.85} \times 100 = 20% \] Thus, number \( B \) is \( \boxed{20%} \) less than number \( A \).