If a man were to sell his chair for Rs. 620, he would loss 20%. To gain 25%, he should sell it for

Options

A. (a) 873.77
B. (b) 968.75
C. (c) 1010.55
D. (d) 1123.36

Answer

To solve the problem step by step, we need to find the cost price (CP) of the chair first and then determine the selling price (SP) required to gain a profit of 25%.

### Step 1: Find the Cost Price (CP) of the Chair
Given that selling the chair for Rs. 620 results in a loss of 20%, we can use the formula for selling price in terms of cost price and loss percentage:

\[ SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]

Substituting the known values:

\[ 620 = CP \times \left(1 - \frac{20}{100}\right) \]

This simplifies to:

\[ 620 = CP \times 0.8 \]

To find CP, we rearrange the equation:

\[ CP = \frac{620}{0.8} \]

Calculating this gives:

\[ CP = 775 \]

### Step 2: Calculate the Selling Price (SP) for a 25% Profit
Now that we have the cost price, we can find the selling price required to achieve a 25% profit using the formula:

\[ SP = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]

Substituting the values we have:

\[ SP = 775 \times \left(1 + \frac{25}{100}\right) \]

This simplifies to:

\[ SP = 775 \times 1.25 \]

Calculating this gives:

\[ SP = 968.75 \]

### Conclusion
To gain a profit of 25%, the chair should be sold for Rs. 968.75.

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