A man buys 7 bats and 6 balls for Rs. 3,800. Later, he buys 3 bats and 5 balls for Rs,. 1,750. What is the cost (in Rs.) of a bat and a ball separately ?

Options

A. Bat : 510, Ball : 40
B. Bat : 480, Ball : 70
C. Bat : 500, Ball : 50
D. Bat : 490, Ball : 60

Answer

To solve the problem of finding the cost of a bat and a ball separately, we can set up a system of equations based on the information given in the question.

### Step-by-Step Solution:

1. **Define Variables:**
Let the cost of one bat be \( x \) (in Rs.) and the cost of one ball be \( y \) (in Rs.).

2. **Set Up Equations:**
From the first purchase, we know:
\[ 7x + 6y = 3800 \quad \text{(Equation 1)} \]
From the second purchase, we have:
\[ 3x + 5y = 1750 \quad \text{(Equation 2)} \]

3. **Multiply Equations to Eliminate One Variable:**
To eliminate \( y \), we can multiply Equation 1 by 5 and Equation 2 by 6:
\[ 5(7x + 6y) = 5(3800) \implies 35x + 30y = 19000 \quad \text{(Equation 3)} \]
\[ 6(3x + 5y) = 6(1750) \implies 18x + 30y = 10500 \quad \text{(Equation 4)} \]

4. **Subtract the Two New Equations:**
Now, we can subtract Equation 4 from Equation 3 to eliminate \( y \):
\[ (35x + 30y) - (18x + 30y) = 19000 - 10500 \]
This simplifies to:
\[ 17x = 8500 \]

5. **Solve for \( x \):**
Dividing both sides by 17 gives:
\[ x = \frac{8500}{17} = 500 \]
Thus, the cost of one bat is Rs. 500.

6. **Substitute \( x \) Back to Find \( y \):**
Now, substitute \( x = 500 \) back into Equation 2 to find \( y \):
\[ 3(500) + 5y = 1750 \]
This simplifies to:
\[ 1500 + 5y = 1750 \]
Subtracting 1500 from both sides gives:
\[ 5y = 250 \]
Dividing both sides by 5 results in:
\[ y = 50 \]
Thus, the cost of one ball is Rs. 50.

### Final Answer:
- The cost of one bat is Rs. 500.
- The cost of one ball is Rs. 50.