Question

A change making machine contains 1 rupee, 2 rupee and 5 rupee coins. The total number of
coins is 300. The amount is Rs. 960. If the number of 1 rupee coins and the number of 2 rupee coins
are interchanged, the value comes down by Rs. 40. The total number of 5 rupee coins is
(1) 100 (2) 140 (3) 60 (4) 150

Answer 1

Answer:

140 coins

Explanation:

Assume that the number of 1 rupee coins is x, the number of 2 rupee coins is y and the number of 5 rupee coins is z

We are given that:

1- The total number of coins is 300:

This means that:

x + y + z = 300

This can be rewritten as:

x = 300 - y - z ...................> equation I

2- The amount is Rs. 960:

This means that:

1x + 2y + 5z = 960 .....................> equation II

Substitute with equation I in equation II as follows:

300 - y - z + 2y + 5z = 960

y + 4z = 660 ..................> equation III

3- If the number of 1 rupee coins and the number of 2 rupee coins are exchanged, the value comes down by Rs. 40

This means that:

1y + 2x + 5z = 960 - 40

y + 2x + 5z = 920 ..................> equation IV

Substitute with equation I in equation IV as follows:

y + 2(300-y-z) + 5z = 920

y + 600 - 2y - 2z + 5z = 920

-y + 3z = 320 ........................> equation V

Add equations III and V and solve for z as follows:

     y + 4z = 660

+   -y + 3z = 320

_______________

           7z = 980

             z = 140

Therefore, the number of 5 rupee coins is 140 coins

Extra work:

Getting the number of 1 rupee coins and 2 rupee coins to check the result.

From equation V:

-y + 3z = 320

-y + 3(140) = 320

-y = -100

y = 100 ...................> number of 2 rupee coins is 100 coins

From equation I:

x = 300 - y - z

x = 300 - 100 - 140 = 60 ................> number of 1 rupee coins is 60 coins

Now, verify the result:

Total number of coins:

x + y + z = 60 + 100 + 140 = 300 coins ............> verified

Total amount:

1x + 2y + 5z = 60 + 2(100) + 5(140) = 960 ...........> verified

Hope this helps :)