By selling a fan for ₹ 600, a man loses `10%` To make a gain of `20%` , the selling price of the fan should be

Options

A. ₹ 800
B. ₹ 900
C. ₹ 1000
D. ₹ 700

Answer

To solve the problem step by step, we need to find the cost price of the fan first and then calculate the selling price required to achieve a 20% profit.

### Step 1: Determine the Cost Price (CP)
Given that the selling price (SP) of the fan is ₹600 and the man incurs a loss of 10%, we can use the formula for loss:

\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \]

Since the loss is 10%, we can express the selling price in terms of the cost price:

\[ \text{Selling Price} = \text{Cost Price} \times \left(1 - \frac{\text{Loss Percentage}}{100}\right) \]

Substituting the values:

\[ 600 = \text{CP} \times \left(1 - \frac{10}{100}\right) \]

This simplifies to:

\[ 600 = \text{CP} \times 0.90 \]

### Step 2: Solve for Cost Price (CP)
Now, we can solve for CP:

\[ \text{CP} = \frac{600}{0.90} \]

Calculating this gives:

\[ \text{CP} = \frac{600 \times 100}{90} = \frac{60000}{90} = 666.67 \text{ (approximately)} \]

### Step 3: Determine the Selling Price for a 20% Profit
To find the selling price that would yield a 20% profit, we use the formula for profit:

\[ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]

Substituting the values:

\[ \text{SP} = \text{CP} \times \left(1 + \frac{20}{100}\right) \]

This simplifies to:

\[ \text{SP} = \text{CP} \times 1.20 \]

Substituting the value of CP we found:

\[ \text{SP} = 666.67 \times 1.20 \]

Calculating this gives:

\[ \text{SP} = 800 \]

### Final Answer
Thus, the selling price of the fan to achieve a 20% profit should be ₹800.

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