Question

A person incurs a loss of 10% when he sells an item for Rs. 1,800. At what price should the item be sold to earn a profit of 10%?

• A. Rs. 2200
• B. Rs. 2100
• C. Rs. 2000
• D. Rs. 1800

Hint:

Find the cost price first from the loss-making sale, then apply the required profit percentage to that same cost price.

Answer 1

The Correct Option is A

This question can be solved without separately writing down the cost price, by comparing the two selling prices directly through a ratio.

A loss of 10 percent means the first selling price equals 90 percent of the cost price. A profit of 10 percent means the second selling price equals 110 percent of the cost price. Since both prices are measured against the same cost price, the ratio of the new selling price to the old selling price is $\frac{110}{90} = \frac{11}{9}$.

The old selling price is given as Rs. 1,800, so the new selling price is

\[ 1800 \times \frac{11}{9} = 200 \times 11 = 2200 \]

Let's check this against the options:

• Rs. 2100 and Rs. 2000 do not match the exact ratio $\frac{11}{9}$ of the old price.
• Rs. 1800 is the loss-making price itself, so it cannot also be the profit-making price.

The item should be sold for Rs. 2,200 to convert the 10 percent loss into a 10 percent profit.