If a man reduces the selling price of a fan from 1,250 to 1,000, his loss increases by 20%. The cost price of the fan is

Options

A. a)2500
B. b)2350
C. c)2400
D. d)2450

Answer

To solve the problem step by step, we need to find the cost price (CP) of the fan given the changes in selling price (SP) and the increase in loss.

### Step 1: Define the variables
Let the cost price of the fan be \( X \).

### Step 2: Identify the selling prices
The original selling price (SP1) is \( 1250 \) and the new selling price (SP2) is \( 1000 \).

### Step 3: Calculate the loss in both scenarios
1. **Loss when SP = 1250:**
\[ \text{Loss1} = X - 1250 \]

2. **Loss when SP = 1000:**
\[ \text{Loss2} = X - 1000 \]

### Step 4: Relate the losses
According to the problem, the loss when the selling price is reduced to \( 1000 \) is \( 20\% \) more than the previous loss. Thus, we can express this relationship as:
\[ \text{Loss2} = \text{Loss1} + 0.2 \times \text{Loss1} \]
This can be rewritten as:
\[ \text{Loss2} = 1.2 \times \text{Loss1} \]

### Step 5: Substitute the loss expressions
Substituting the expressions for Loss1 and Loss2:
\[ X - 1000 = 1.2 \times (X - 1250) \]

### Step 6: Simplify the equation
Distributing \( 1.2 \) on the right side:
\[ X - 1000 = 1.2X - 1500 \]

### Step 7: Rearranging the equation
Now, we can rearrange the equation to isolate \( X \):
\[ X - 1.2X = -1500 + 1000 \]
\[ -0.2X = -500 \]

### Step 8: Solve for \( X \)
Dividing both sides by \( -0.2 \):
\[ X = \frac{-500}{-0.2} = 2500 \]

### Conclusion
The cost price of the fan is \( 2500 \).