A box contains Rs. 56 of Rs. 1, 50p and 25p. The number of 50p coins is double of 25p coins and 4 times of Rs. 1 coins. Then what is the number of 50p coins?

Options

A. 12
B. 64
C. 128
D. 60

Answer

To solve the problem step by step, we will define the variables for each type of coin and set up equations based on the information given.

### Step 1: Define the variables
Let:
- \( x \) = number of Rs. 1 coins
- \( y \) = number of 50p coins
- \( z \) = number of 25p coins

### Step 2: Establish relationships between the variables
According to the problem:
1. The number of 50p coins is double the number of 25p coins:
\[ y = 2z \]
2. The number of 50p coins is four times the number of Rs. 1 coins:
\[ y = 4x \]

### Step 3: Write the total value equation
The total value of the coins is Rs. 56. We need to convert all values to the same unit (paisa) for easier calculation:
- Rs. 1 = 100 paisa
- 50p = 50 paisa
- 25p = 25 paisa

Thus, the total value in paisa is:
\[ 100x + 50y + 25z = 5600 \quad \text{(since Rs. 56 = 5600 paisa)} \]

### Step 4: Substitute the relationships into the total value equation
Substituting \( y = 2z \) into \( y = 4x \):
\[ 2z = 4x \implies z = 2x \]

Now substitute \( y \) and \( z \) in terms of \( x \) into the total value equation:
\[ 100x + 50(2z) + 25z = 5600 \]
Substituting \( z = 2x \):
\[ 100x + 50(2(2x)) + 25(2x) = 5600 \]
This simplifies to:
\[ 100x + 200x + 50x = 5600 \]
\[ 350x = 5600 \]

### Step 5: Solve for \( x \)
\[ x = \frac{5600}{350} = 16 \]

### Step 6: Find \( y \) (number of 50p coins)
Now that we have \( x \), we can find \( y \):
Using \( y = 4x \):
\[ y = 4 \times 16 = 64 \]

### Step 7: Conclusion
The number of 50p coins is \( \boxed{64} \).

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