A purse contains a cetain number of coins fo denominations Re. 1 and 50 paise. The total value of the coins (in Rs) is 14 less than the total number of coins. Find the number of 50 paise coins

Options

A. 12
B. 18
C. 22
D. 28

Explanation

To solve the problem, we need to find the number of 50 paise coins in a purse that contains both Re. 1 and 50 paise coins. Let's denote:

- Let \( x \) be the number of Re. 1 coins.
- Let \( y \) be the number of 50 paise coins.

### Step 1: Write the equations based on the problem statement.

1. The total number of coins is \( x + y \).
2. The total value of the coins in Rupees is given by:
- Value of Re. 1 coins = \( x \times 1 = x \) Rs.
- Value of 50 paise coins = \( y \times 0.5 = 0.5y \) Rs.
- Therefore, the total value of the coins = \( x + 0.5y \) Rs.

According to the problem, the total value of the coins is Rs. 14 less than the total number of coins. This gives us the equation:
\[ x + 0.5y = (x + y) - 14 \]

### Step 2: Simplify the equation.

Rearranging the equation from Step 1:
\[ x + 0.5y = x + y - 14 \]
Subtract \( x \) from both sides:
\[ 0.5y = y - 14 \]
Now, subtract \( y \) from both sides:
\[ 0.5y - y = -14 \]
This simplifies to:
\[ -0.5y = -14 \]

### Step 3: Solve for \( y \).

To isolate \( y \), multiply both sides by -1:
\[ 0.5y = 14 \]
Now, divide both sides by 0.5:
\[ y = \frac{14}{0.5} = 28 \]

### Step 4: Conclusion.

Thus, the number of 50 paise coins is \( y = 28 \).