A man has 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount is 160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?
Question
A man has 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount is 160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?
Solution
Let's denote:
- The number of 25 paise coins as x
- The number of 50 paise coins as y
- The number of 1 Rupee coins as z
From the problem, we have the following three equations:
- x + y + z = 220 (since there are 220 coins in total)
- 0.25x + 0.50y + z = 160 (since the total amount is 160 Rupees)
- z = 3x (since there are thrice as many 1 Rupee coins as there are 25 paise coins)
We can substitute equation 3 into equations 1 and 2 to get:
- x + y + 3x = 220
- 0.25x + 0.50y + 3x = 160
Solving these equations gives:
- 4x + y = 220
- 3.25x + 0.50y = 160
Multiplying equation 2 by 2 gives:
6.5x + y = 320
Subtracting equation 1 from this gives:
2.5x = 100
So, x = 40.
Substituting x = 40 into equation 1 gives:
4*40 + y = 220 160 + y = 220 y = 220 - 160 = 60
So, the number of 50 paise coins is 60.
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