Question

A salesman's terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs. 1,000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per the new scheme was Rs. 600 more than by the first scheme, what were his sales worth?

• A. Rs. 11,000
• B. Rs. 17,000
• C. Rs. 16,000
• D. Rs. 12,000

Hint:

For commission problems, set up the equations for both commission structures and compare earnings.

Answer 1

The Correct Option is D

Let total sales be \( x \).
Under the first scheme: \[ \text{Commission} = 5% \times x = 0.05x \] Under the new scheme: - Fixed salary = Rs. 1,000 - Commission on \( x - 4,000 \) = \( 2.5% \) \[ 1,000 + 0.025(x - 4,000) \] The difference between the two earnings is Rs. 600: \[ 1,000 + 0.025(x - 4,000) = 0.05x + 600 \] \[ 1,000 + 0.025x - 100 = 0.05x + 600 \] \[ 900 + 0.025x = 0.05x + 600 \] \[ 900 - 600 = 0.05x - 0.025x \] \[ 300 = 0.025x \] \[ x = \frac{300}{0.025} = 12,000 \] Thus, the total sales were Rs. 12,000.