An overall profit of 25.5% is to be made from the sale of two products. One of them was sold at a loss of 8.5%. At what profit percentage should the second product be sold, given that the cost prices of the first and the second products are in the ratio 3:5?

Correct option is D

Given:
Overall profit = 25.5%
First product sold at a loss of 8.5%
Cost price ratio of first and second products = 3:5

Concept Used:
The weighted average profit/loss percentage is calculated using the given ratio of cost prices.

Solution:

​$$\frac{(3 \times (-8.5)) + (5 \times x)}{3+5} = 25.5$$​​

​$$\frac{(3 \times -8.5) + (5 \times x)}{8} = 25.5$$​​

​$$\frac{-25.5 + 5x}{8} = 25.5$$​​

-25.5 + 5x = 204

5x = 229.5

x = 45.9

So. the second product should be sold at a profit of 45.9%.

Thus, the correct answer is (d).

Alternative Method;

Let profit = x

Since the ratio of cost prices is given as 3:5, we equate:

​$$\frac{3}{5} = \frac{x - 25.5} {34}$$

3 × 34 = 5 × (x - 25.5)

102 = 5x - 127.5

5x = 102 + 127.5

5x = 229.5

x = 45.9