A piggy bank contains an equal number of one rupee,50 paise and 25 paise coins. If the total value of Rs. 56, then how many coins of each type are there?

Options

A. 25
B. 32
C. 30
D. 22

Answer

To solve the problem step by step, let's denote the number of each type of coin as \( x \).

### Step 1: Identify the values of the coins
- The value of one 1 rupee coin is \( 1 \) rupee.
- The value of one 50 paise coin is \( 0.5 \) rupees (since 50 paise is half of a rupee).
- The value of one 25 paise coin is \( 0.25 \) rupees (since 25 paise is a quarter of a rupee).

### Step 2: Write the equation for total value
Since there are \( x \) coins of each type, we can express the total value of the coins as follows:
\[ \text{Total value} = (\text{Number of 1 rupee coins} \times \text{Value of 1 rupee coin}) + (\text{Number of 50 paise coins} \times \text{Value of 50 paise coin}) + (\text{Number of 25 paise coins} \times \text{Value of 25 paise coin}) \]
This translates to:
\[ x \cdot 1 + x \cdot 0.5 + x \cdot 0.25 = 56 \]

### Step 3: Simplify the equation
Now, we can simplify the equation:
\[ x + 0.5x + 0.25x = 56 \]
Combining the terms on the left side:
\[ (1 + 0.5 + 0.25)x = 56 \]
Calculating the sum:
\[ 1.75x = 56 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides by 1.75:
\[ x = \frac{56}{1.75} \]
Calculating the division:
\[ x = 32 \]

### Step 5: Conclusion
Thus, the number of each type of coin (1 rupee, 50 paise, and 25 paise) is \( 32 \).