A sum of Rs. 36.90 is made up of 180 coins which are either 10 paise coins or 25 paise coins. Determine the number of each type of coins.

Options

A. 126 of 10 p coins and 54 of 25 p coins
B. 54 of 10 p coins and 126 of 25 p coins
C. 90 of 10 p coins and 90 of 25 p coins
D. 54 of 10 p coins and 90 of 25 p coins

Answer

To solve the problem of determining the number of 10 paise and 25 paise coins that make up a total of Rs. 36.90 using 180 coins, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = number of 10 paise coins
- \( y \) = number of 25 paise coins

### Step 2: Set Up Equations
From the problem, we know:
1. The total number of coins is 180:
\[ x + y = 180 \quad \text{(Equation 1)} \]

2. The total value of the coins is Rs. 36.90. Since 1 rupee = 100 paise, Rs. 36.90 = 3690 paise:
\[ 10x + 25y = 3690 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 1 for \( y \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 180 - x \]

### Step 4: Substitute \( y \) in Equation 2
Now, substitute \( y \) in Equation 2:
\[ 10x + 25(180 - x) = 3690 \]

### Step 5: Simplify the Equation
Distributing the 25:
\[ 10x + 4500 - 25x = 3690 \]
Combine like terms:
\[ -15x + 4500 = 3690 \]

### Step 6: Isolate \( x \)
Subtract 4500 from both sides:
\[ -15x = 3690 - 4500 \]
\[ -15x = -810 \]
Now, divide by -15:
\[ x = \frac{810}{15} \]
\[ x = 54 \]

### Step 7: Find \( y \)
Now substitute \( x \) back to find \( y \):
\[ y = 180 - x = 180 - 54 = 126 \]

### Conclusion
Thus, the number of 10 paise coins is \( 54 \) and the number of 25 paise coins is \( 126 \).

### Summary of Results
- Number of 10 paise coins: **54**
- Number of 25 paise coins: **126**