A person bought 2 fans for Rs 2160. After selling first fan at 15% profit and second at 9% loss he neither gains nor looses . Find C.P. of each fan?

Answer

To solve the problem, we need to find the cost price (C.P.) of each fan given that a person bought two fans for Rs 2160, sold the first fan at a 15% profit, and the second fan at a 9% loss, resulting in no overall gain or loss.

### Step-by-Step Solution:

1. **Let the Cost Price of the First Fan be \( x \)** and the Cost Price of the Second Fan be \( y \).
- We know that \( x + y = 2160 \) (since the total cost price of both fans is Rs 2160).

2. **Calculate Selling Price of the First Fan**:
- Selling Price (S.P.) of the first fan = Cost Price + Profit
- Profit = 15% of \( x \) = \( 0.15x \)
- Therefore, S.P. of the first fan = \( x + 0.15x = 1.15x \).

3. **Calculate Selling Price of the Second Fan**:
- Selling Price (S.P.) of the second fan = Cost Price - Loss
- Loss = 9% of \( y \) = \( 0.09y \)
- Therefore, S.P. of the second fan = \( y - 0.09y = 0.91y \).

4. **Set Up the Equation for No Profit No Loss**:
- Since there is no overall gain or loss, the total selling price of both fans equals the total cost price.
- Thus, we can write the equation:
\[ 1.15x + 0.91y = 2160 \]

5. **Now we have a system of equations**:
- Equation 1: \( x + y = 2160 \)
- Equation 2: \( 1.15x + 0.91y = 2160 \)

6. **Substituting Equation 1 into Equation 2**:
- From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 2160 - x \]
- Substitute \( y \) in Equation 2:
\[ 1.15x + 0.91(2160 - x) = 2160 \]

7. **Simplifying the Equation**:
- Distributing \( 0.91 \):
\[ 1.15x + 1965.6 - 0.91x = 2160 \]
- Combine like terms:
\[ (1.15 - 0.91)x + 1965.6 = 2160 \]
\[ 0.24x + 1965.6 = 2160 \]

8. **Isolate \( x \)**:
- Subtract \( 1965.6 \) from both sides:
\[ 0.24x = 2160 - 1965.6 \]
\[ 0.24x = 194.4 \]
- Divide by \( 0.24 \):
\[ x = \frac{194.4}{0.24} = 810 \]

9. **Finding \( y \)**:
- Substitute \( x \) back into Equation 1:
\[ y = 2160 - 810 = 1350 \]

10. **Final Cost Prices**:
- Cost Price of the First Fan \( (x) = 810 \)
- Cost Price of the Second Fan \( (y) = 1350 \)

### Summary of Results:
- C.P. of the First Fan = Rs 810
- C.P. of the Second Fan = Rs 1350