A box contains ₹ 56 in the form of coins of one rupee, 50 paise and 25 paise. The number of 50 paise coin is double the number of 25 paise coins and four times the numbers of one rupee coins. The numbers of 50 paise coins in the box is
Question
A box contains ₹ 56 in the form of coins of one rupee, 50 paise and 25 paise. The number of 50 paise coin is double the number of 25 paise coins and four times the numbers of one rupee coins. The numbers of 50 paise coins in the box is
Solution
Let's denote the number of one rupee coins as x, the number of 50 paise coins as y, and the number of 25 paise coins as z.
From the problem, we know that:
- y = 2z (The number of 50 paise coins is double the number of 25 paise coins)
- y = 4x (The number of 50 paise coins is four times the number of one rupee coins)
Since y = 4x, we can substitute y in the first equation to get: 4x = 2z, which simplifies to z = 2x.
The total value of the coins is ₹56, which is equal to 5600 paise. We can express this total value in terms of x, y, and z:
100x + 50y + 25z = 5600
Substituting y = 4x and z = 2x into this equation gives:
100x + 50(4x) + 25(2x) = 5600 100x + 200x + 50x = 5600 350x = 5600 x = 5600 / 350 x = 16
Substituting x = 16 into y = 4x gives y = 4*16 = 64.
So, the number of 50 paise coins in the box is 64.
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