Final answer:
The problem involves creating and solving a system of linear equations based on conversions between rupees and paise and given conditions relating different coin denominations. The solution is that there are 32 fifty paise coins in the box.
Step-by-step explanation:
The student is asking about a problem related to coin denominations and linear equations. In Indian currency, the conversion is: 1 rupee (Rs) = 100 paise. Given the conditions in the problem, let us denote the number of 25 paise coins as x, the number of 50 paise coins as y, and the number of one rupee coins as z. The total value is Rs. 56, which can be converted into paise by multiplying by 100, giving us 5600 paise. We know that the number of 50 paise coins is double the number of 25 paise coins (y = 2x), and four times the number of one rupee coins (y = 4z).
Using this information, we can create the following equations:
- 25x + 50y + 100z = 5600 (total value)
- y = 2x (relation between 50 p and 25 p coins)
- y = 4z (relation between 50 p and one rupee coins)
By substituting y from equations (2) and (3) into equation (1), we can solve for the number of coins. After solving the equations, we find that the number of 50 paise coins is 32.
Therefore answer is C. 32.