Question

A man went to market to purchase bats and balls.

The cost of one bat is Rs. 500 and cost of one ball is Rs. 50. If he spent Rs. 1750 on 8 items. How many bats and balls he

purchased?
​

Answer 1

Step-by-step explanation:

Given:

A man went to market to purchase bats and balls. The cost of one bats is ₹500 and cost of one balls is ₹50. If he spent ₹1750 of 8 items.

To find: How many bats and balls he purchased?

Solution:

Let x number of balls and y number of bats are purchased.

ATQ

Total 8 items were purchased.

Thus,

$\begin{gathered}\bold{x + y = 8} \: \: ...eq1\\ \end{gathered}$

Cost of one bat is 500 Rs,so cost of y bats =500y Rs

Cost of one ball is 50 Rs,so cost of x balls =50x Rs

So,

$\bold{50x + 500y = 1750} \: \: ...eq2$

Now,solve these two equation

Multiply eq1 by 50 and subtract eq2-eq1

$\begin{gathered}50x + 500y = 1750 \\ 50x + 50y = 400 \: \: \: \: \\ ( - ) \: \: \: \: \: \: ( - ) \: \: \: \: \:\: ( - ) \\ - - - - - - - - \\ 450y = 1350 \\ \\ y = \frac{1350}{450} \\ \\ \boxed{\bold{y = 3}} \\ \\ \end{gathered}$

put the value of y in eq1

$\begin{gathered}x + y = 8 \\ \\ x + 3 = 8 \\ \\ x = 8 - 3 \\ \\ \boxed{\bold{x = 5}} \\ \\ \end{gathered}$

Final answer:

No. of balls purchased: 5

No. of bats purchased: 3

Verification:

= 5×50+3×500

= 250+1500

= 1750 Rs

Hope it helps you.

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