Rahim sells chair at a gain of `(7)1/2%` . If he had bought it at `(12)1/2%` loss and sold it for Rs. 5 more. He would have gained `30%`. The C.P. of the chair is

Options

A. Rs. 72
B. Rs. 80
C. Rs. 88
D. Rs. 96

Answer

To find the Cost Price (C.P.) of the chair, we will follow these steps:

### Step 1: Define the Cost Price
Let the Cost Price (C.P.) of the chair be Rs. 100.

### Step 2: Calculate Selling Price (S.P.) with 7.5% Gain
Rahim sells the chair at a gain of \(7.5\%\).
- The Selling Price (S.P.) can be calculated as:
\[ S.P. = C.P. + \text{Gain} = 100 + \left( \frac{7.5}{100} \times 100 \right) = 100 + 7.5 = 107.5 \]

### Step 3: Calculate New Cost Price with 12.5% Loss
If Rahim had bought the chair at a \(12.5\%\) loss, the new Cost Price (New C.P.) would be:
- New C.P. = \(C.P. - \text{Loss}\)
\[ \text{New C.P.} = 100 - \left( \frac{12.5}{100} \times 100 \right) = 100 - 12.5 = 87.5 \]

### Step 4: Calculate Selling Price for 30% Gain
If he sold it for Rs. 5 more than the original S.P. and gained \(30\%\), we can find the new Selling Price (New S.P.):
- New S.P. = New C.P. + Gain
\[ \text{New S.P.} = 87.5 + \left( \frac{30}{100} \times 87.5 \right) = 87.5 + 26.25 = 113.75 \]

### Step 5: Set Up the Equation
According to the problem, the difference between the new S.P. and the original S.P. is Rs. 5:
\[ \text{New S.P.} - \text{Original S.P.} = 5 \]
Substituting the values we calculated:
\[ 113.75 - 107.5 = 5 \]
This confirms our calculations are correct.

### Step 6: Calculate the Value of 1 Unit
Now, we know that the difference of Rs. 5 corresponds to a certain number of units. We can find the value of 1 unit:
- The difference in S.P. is Rs. 5, and we need to find out how many units this corresponds to.
- The profit per unit is:
\[ \text{Profit per unit} = \frac{5}{113.75 - 107.5} = \frac{5}{6.25} = 0.8 \]

### Step 7: Calculate the Cost Price
Now, we can find the actual Cost Price based on the unit value:
- If 100 units correspond to Rs. 5, then:
\[ \text{C.P.} = \frac{5}{6.25} \times 100 = 80 \]

### Conclusion
Thus, the Cost Price (C.P.) of the chair is Rs. 80.

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