On selling a fan for Rs. 1620, a shopkeeper losses 10%. For what amount should he sell it to gain 5%?

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the fan based on the information given about the selling price (SP) and the loss percentage. Then, we will calculate the new selling price needed to achieve a gain of 5%.

### Step 1: Determine the Cost Price (CP)

Given:
- Selling Price (SP) = Rs. 1620
- Loss Percentage = 10%

We know that:
Loss = CP - SP

From the loss percentage formula:
Loss Percentage = (Loss / CP) × 100

Substituting the values:
10 = (Loss / CP) × 100

This means:
Loss = (10/100) × CP = CP / 10

Now, substituting the loss in the loss formula:
Loss = CP - SP
CP / 10 = CP - 1620

### Step 2: Solve for CP

Rearranging the equation:
CP - CP / 10 = 1620

To combine the terms, we can write CP as 10CP/10:
(10CP/10) - (CP/10) = 1620
(10CP - CP) / 10 = 1620
(9CP) / 10 = 1620

Now, multiply both sides by 10:
9CP = 16200

Now, divide by 9:
CP = 16200 / 9
CP = 1800

### Step 3: Calculate the Selling Price for a Gain of 5%

Now that we have the cost price (CP = Rs. 1800), we can find the selling price (SP) for a gain of 5%.

Gain Percentage = 5%
Gain = (Gain Percentage / 100) × CP
Gain = (5 / 100) × 1800
Gain = 90

### Step 4: Determine the New Selling Price

Using the gain to find the new selling price:
SP = CP + Gain
SP = 1800 + 90
SP = 1890

### Final Answer

The shopkeeper should sell the fan for Rs. 1890 to gain 5%.

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