A bag contain equal number of 1 rupee, 50 paisa and 25 paisa coins. If the total amount is Rs 105, then how many coins of each type are there?

Options

A. 15
B. 45
C. 60
D. 80

Answer

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

### Step 1: Define the number of coins
Let:
- Number of 1 rupee coins = \( x \)
- Number of 50 paisa coins = \( x \)
- Number of 25 paisa coins = \( x \)

### Step 2: Calculate the total value of the coins
Now, we can calculate the total value contributed by each type of coin:
- Value from 1 rupee coins = \( 1 \times x = x \) rupees
- Value from 50 paisa coins = \( 0.50 \times x = 0.5x \) rupees
- Value from 25 paisa coins = \( 0.25 \times x = 0.25x \) rupees

### Step 3: Set up the equation for total value
The total value of all the coins is given as Rs 105. Therefore, we can set up the equation:
\[ x + 0.5x + 0.25x = 105 \]

### Step 4: Combine like terms
Now, combine the terms on the left side:
\[ (1 + 0.5 + 0.25)x = 105 \]
\[ 1.75x = 105 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 1.75:
\[ x = \frac{105}{1.75} \]

### Step 6: Calculate \( x \)
Calculating the division:
\[ x = 60 \]

### Conclusion
Thus, the number of coins of each type is \( 60 \).