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 sold it at a discount of 10%. In this deal, the man reduced Rs. 70 in profit. What was the market value of the bat?

Options

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

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define the Market Value
Let the market value of the bat be \( X \) rupees.

### Step 2: Calculate Selling Price with 8% Discount
When the man sells the bat at an 8% discount, the selling price (SP1) can be calculated as:
\[ SP1 = X - 0.08X = 0.92X \]

### Step 3: Calculate Selling Price with 10% Discount
When the man sells the bat at a 10% discount to his brother, the selling price (SP2) can be calculated as:
\[ SP2 = X - 0.10X = 0.90X \]

### Step 4: Establish the Profit Relationship
According to the problem, the profit from selling to his brother (SP2) is Rs. 70 less than the profit from selling at the 8% discount (SP1). Therefore, we can set up the equation:
\[ (SP1 - CP) - (SP2 - CP) = 70 \]
This simplifies to:
\[ SP1 - SP2 = 70 \]

### Step 5: Substitute Selling Prices
Now, substitute the values of SP1 and SP2 into the equation:
\[ 0.92X - 0.90X = 70 \]

### Step 6: Simplify the Equation
This simplifies to:
\[ 0.02X = 70 \]

### Step 7: Solve for X
To find \( X \), divide both sides by 0.02:
\[ X = \frac{70}{0.02} = 3500 \]

### Conclusion
Thus, the market value of the bat is:
\[ \text{Market Value} = 3500 \text{ rupees} \]