A person sold an article at a loss of 15%. Had he sold it for Rs. 30.60 more, he would have gained 9%. To gain 10%, he should have sold it for:

Steps to Solve

1. Identify Loss and Gain Percentages

The article is sold at a loss of 15% and can be sold at a gain of 9% if sold at a price Rs. 30.60 more.

2. Set Up the Equation for Selling Price

Let the cost price (CP) be $x$. The selling price (SP) at a 15% loss is given by:

$$ SP_{loss} = x - 0.15x = 0.85x $$

3. Calculate Selling Price for 9% Gain

Selling the article for Rs. 30.60 more would yield a selling price for a 9% gain:

$$ SP_{gain} = x + 0.09x = 1.09x $$

Now we know:

$$ SP_{gain} = SP_{loss} + 30.60 $$

Substituting the equations, we get:

$$ 1.09x = 0.85x + 30.60 $$

4. Solve the Equation for Cost Price

Rearranging the equation:

$$ 1.09x - 0.85x = 30.60 $$

This simplifies to:

$$ 0.24x = 30.60 $$

Then, we find $x$:

$$ x = \frac{30.60}{0.24} = 127.5 $$

5. Find Selling Price for 10% Profit

Now, for a 10% profit, the selling price is:

$$ SP_{10%} = CP + 0.10 \times CP = 1.10x $$

Substituting the value of $x$:

$$ SP_{10%} = 1.10 \times 127.5 = 140.25 $$