By selling a watch for Rs. 1440, a man losses 10%. At what price should he sell it to gain 10%?

Answer

To solve the problem step by step, we need to find the cost price (CP) of the watch first and then calculate the selling price (SP) required to achieve a 10% gain.

### Step 1: Find the Cost Price (CP)
We know that the selling price (SP) is Rs. 1440 and the man incurs a loss of 10%.

To find the cost price when there is a loss, we can use the formula:
\[ CP = \frac{100}{100 - \text{Loss Percentage}} \times SP \]

Substituting the values:
\[ CP = \frac{100}{100 - 10} \times 1440 \]
\[ CP = \frac{100}{90} \times 1440 \]
\[ CP = \frac{100 \times 1440}{90} \]
\[ CP = \frac{144000}{90} \]
\[ CP = 1600 \]

### Step 2: Calculate the Selling Price for a 10% Gain
Now that we have the cost price (CP = Rs. 1600), we need to find the selling price (SP) that would give a 10% gain.

To find the selling price when there is a gain, we can use the formula:
\[ SP = \frac{100 + \text{Gain Percentage}}{100} \times CP \]

Substituting the values:
\[ SP = \frac{100 + 10}{100} \times 1600 \]
\[ SP = \frac{110}{100} \times 1600 \]
\[ SP = 1.1 \times 1600 \]
\[ SP = 1760 \]

### Final Answer
The man should sell the watch for Rs. 1760 to gain 10%.

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