A bag contain 20 coins of denominations of 50 paise and 1 rupees . The total value of the coin in the bag is 16 rupees . Find the number of coins of each denomination.?

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Answer

Problem Statement:
A bag contains 20 coins of denominations of 50 paise and 1 rupee. The total value of the coins in the bag is 16 rupees. Find the number of coins of each denomination.

Solution:
To solve this problem, we can use the method of simultaneous equations. Let's assume the number of 50 paise coins as 'x' and the number of 1 rupee coins as 'y'.

Equation 1:
The total number of coins is given as 20. So, we have:
x + y = 20

Equation 2:
The total value of the coins is given as 16 rupees. The value of a 50 paise coin is 0.50 rupees and the value of a 1 rupee coin is 1 rupee. So, the equation becomes:
0.50x + 1y = 16

Now, we can solve these two equations simultaneously to find the values of 'x' and 'y'.

Solving the equations:
We can solve these equations by substitution or elimination method. Let's use the elimination method here.

Multiplying Equation 1 by -0.50, we get:
-0.50x - 0.50y = -10

Adding this equation to Equation 2, we get:
-0.50x - 0.50y + 0.50x + y = -10 + 16
0.50y = 6
y = 6/0.50
y = 12

Substituting the value of y in Equation 1, we get:
x + 12 = 20
x = 20 - 12
x = 8

Therefore, the number of 50 paise coins is 8 and the number of 1 rupee coins is 12.

Answer:
The number of coins of each denomination is as follows:
- 50 paise coins: 8
- 1 rupee coins: 12

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