On selling a bat for Rs. 742, a man gains 6%. For how much should he sell it to gain 8 %

Answer

To solve the problem step by step, let's follow the logical sequence of calculations.

### Step 1: Understand the Given Information
- Selling Price (SP) = Rs. 742
- Gain Percentage (GP) = 6%

### Step 2: Calculate the Cost Price (CP)
To find the Cost Price (CP), we can use the formula:
\[ CP = \frac{100}{100 + GP} \times SP \]
Substituting the values:
\[ CP = \frac{100}{100 + 6} \times 742 \]
\[ CP = \frac{100}{106} \times 742 \]
Now, calculate:
\[ CP = \frac{74200}{106} \approx 700 \]
So, the Cost Price is Rs. 700.

### Step 3: Calculate the New Selling Price for 8% Gain
Now we need to find the Selling Price (SP) for an 8% gain. We can use the formula:
\[ SP = \frac{100 + GP}{100} \times CP \]
Substituting the values:
\[ SP = \frac{100 + 8}{100} \times 700 \]
\[ SP = \frac{108}{100} \times 700 \]
Now, calculate:
\[ SP = 1.08 \times 700 = 756 \]
So, the Selling Price for an 8% gain should be Rs. 756.

### Final Answer
The man should sell the bat for Rs. 756 to gain an 8%.

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