In a bag there are coins of 25 paisa, 50 paisa and 1 rupee in the ratio of 3:4:5. If there are in all ₹ 31, then how many 1 rupee coins are there in the bag?
- A12
- B16
- C24
- D20
Solution & Step-by-step Explanation
Let the number of 25 paisa, 50 paisa, and 1 rupee coins be 3x,4x, and 5x respectively.
Convert the value of each denomination into rupees:
Value of 25 paisa coins = 3x×0.25=0.75x
Value of 50 paisa coins = 4x×0.50=2.00x
Value of 1 rupee coins = 5x×1.00=5.00x
The total value of all coins is ₹ 31:
0.75x+2.00x+5.00x=31
7.75x=31
Solving for x:
x=
7.75
31
=
4
31
31
=4
The number of 1 rupee coins is 5x:
Number of 1 rupee coins=5×4=20
Convert the value of each denomination into rupees:
Value of 25 paisa coins = 3x×0.25=0.75x
Value of 50 paisa coins = 4x×0.50=2.00x
Value of 1 rupee coins = 5x×1.00=5.00x
The total value of all coins is ₹ 31:
0.75x+2.00x+5.00x=31
7.75x=31
Solving for x:
x=
7.75
31
=
4
31
31
=4
The number of 1 rupee coins is 5x:
Number of 1 rupee coins=5×4=20