Cost of Each Bat and Each Ball

Video Explanation

Question

The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later, he buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.

Solution

Step 1: Let the Variables

Let the cost of one bat = Rs \(x\)

Let the cost of one ball = Rs \(y\)

Step 2: Form the Equations

\[ 7x + 6y = 3800 \quad (1) \]

\[ 3x + 5y = 1750 \quad (2) \]

Step 3: Solve by Elimination Method

Multiply equation (2) by 7:

\[ 21x + 35y = 12250 \quad (3) \]

Multiply equation (1) by 3:

\[ 21x + 18y = 11400 \quad (4) \]

Subtract equation (4) from (3):

\[ (21x + 35y) – (21x + 18y) = 12250 – 11400 \]

\[ 17y = 850 \]

\[ y = 50 \]

Step 4: Find the Value of x

Substitute \(y = 50\) in equation (2):

\[ 3x + 5(50) = 1750 \]

\[ 3x + 250 = 1750 \]

\[ 3x = 1500 \]

\[ x = 500 \]

Conclusion

Cost of one bat:

\[ \boxed{Rs\; 500} \]

Cost of one ball:

\[ \boxed{Rs\; 50} \]

Final Answer (For Exam)

Cost of one bat = Rs 500
Cost of one ball = Rs 50