Question

The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later she buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.
(a) The cost of each bat is Rs.800 and the cost of each ball is Rs.80
(b) The cost of each bat is Rs.750 and the cost of each ball is Rs.120
(c) The cost of each bat is Rs.600 and the cost of each ball is Rs.150
(d) The cost of each bat is Rs.500 and the cost of each ball is Rs.50

Answer 1

Hint:First we will take some variable x for the cost of each bat and y for the cost of each ball. And then we will write the equations with given information i.e total sum of money of 7x bats and 6y balls is Rs3800 and 3x bats and 5 balls is Rs1750 given in the question. And then we will solve these two equations to find the value of each bat and each ball.

Complete step-by-step answer:
Let x = price of each bat and y = price of each ball.
Now we know that the cost of 7 bats and 6 balls is Rs. 3800
Hence, we get
$7x+6y=3800...........(1)$
Now for the second equation we have the cost of 3 bats and 5 balls is Rs. 1750
Hence, we get
$3x+5y=1750..........(2)$
First we will find the value of x.
Now multiplying equation (1) by 5 and equation (2) by 6 and subtracting these two equations
$5\times eq(1)-6\times eq(2)$ we get,
$\begin{align}
  & 35x+30y-\left( 18x+30y \right)=3800\times 5-1750\times 6 \\
 & 17x=8500 \\
 & x=500 \\
\end{align}$
Hence, the cost of each bat is Rs.500
Now we will put the value of x in equation (2) we get,
$\begin{align}
  & 3\times 500+5y=1750 \\
 & 5y=1750-1500 \\
 & 5y=250 \\
 & y=50 \\
\end{align}$
Hence, the cost of each ball is Rs.50
Therefore, option (d) is correct.

Note: We have used the method of solving two equations in two variables algebraically, one can also solve the equations using the matrix method or elimination method i.e.writing x in terms of y and substituting in (2) equation we get the value of y, but it will take a huge amount of time and will also increase the chance of making mistakes.