A man wanted to sell his bat at a discount of 8%. His brother who was a cricketer wanted to buy the bat, so the man sells it at a discount of 10%. In this deal, the man reduces Rs.70 in profit. What was the market value of the bat?

Options

A. Rs. 3,200
B. Rs. 2,500
C. Rs. 3,000
D. Rs. 3,500

Answer

To solve the problem step by step, let's denote the market value of the bat as \( x \).

### Step 1: Calculate Selling Price at 8% Discount
The man initially wanted to sell the bat at a discount of 8%. Therefore, the selling price (SP) at this discount can be calculated as:
\[ SP_{8\%} = x - (8\% \text{ of } x) = x - 0.08x = 0.92x \]

### Step 2: Calculate Selling Price at 10% Discount
When the man sells the bat to his brother at a discount of 10%, the selling price becomes:
\[ SP_{10\%} = x - (10\% \text{ of } x) = x - 0.10x = 0.90x \]

### Step 3: Determine the Reduction in Profit
According to the problem, selling at a 10% discount results in a reduction of Rs. 70 in profit. This means:
\[ SP_{8\%} - SP_{10\%} = 70 \]
Substituting the selling prices we calculated:
\[ 0.92x - 0.90x = 70 \]

### Step 4: Simplify the Equation
Now, simplify the equation:
\[ 0.02x = 70 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 0.02:
\[ x = \frac{70}{0.02} = 3500 \]

### Conclusion
The market value of the bat is Rs. 3500.

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