By selling a fan for Rs. 1900 a man has a lose of 5%, then at what price (in Rs.) should he sell the fan to gain 20%?

Options

A. 2000
B. 2400
C. 2600
D. 2800

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Loss Situation
We know that the selling price (SP) of the fan is Rs. 1900, and the man incurs a loss of 5%.

**Hint:** Remember that a loss of 5% means he sold the fan for 95% of its cost price (CP).

### Step 2: Set Up the Equation for Cost Price
Since he sold the fan for Rs. 1900 at a loss of 5%, we can express this as:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
Substituting the values:
\[ 1900 = CP \times \left(1 - \frac{5}{100}\right) \]
This simplifies to:
\[ 1900 = CP \times 0.95 \]

**Hint:** To find the cost price (CP), you will need to isolate CP in the equation.

### Step 3: Calculate the Cost Price
Now, we can solve for CP:
\[ CP = \frac{1900}{0.95} \]
Calculating this gives:
\[ CP = 2000 \]

**Hint:** Make sure to perform the division carefully to get the correct value of CP.

### Step 4: Set Up the Equation for Gain Situation
Next, we want to find the selling price for a gain of 20%. The selling price in this case can be expressed as:
\[ SP = CP \times \left(1 + \frac{Gain\%}{100}\right) \]
Substituting the values:
\[ SP = 2000 \times \left(1 + \frac{20}{100}\right) \]
This simplifies to:
\[ SP = 2000 \times 1.20 \]

**Hint:** Remember that a gain of 20% means he sold the fan for 120% of its cost price.

### Step 5: Calculate the New Selling Price
Now, we can calculate the new selling price:
\[ SP = 2000 \times 1.20 = 2400 \]

**Hint:** Ensure to multiply correctly to find the final selling price.

### Final Answer
Thus, the price at which he should sell the fan to gain 20% is **Rs. 2400**.

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