A total of 324 coins of 20 paise and 25 paise make a sum of Rs. 71, then number of 20 paise coins is :

Options

A. 124
B. 140
C. 200
D. 210

Answer

To solve the problem step by step, we can set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( x \) = number of 20 paise coins
- \( y \) = number of 25 paise coins

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of coins is 324:
\[ x + y = 324 \quad \text{(1)} \]
2. The total value of the coins is Rs. 71, which is equal to 7100 paise:
\[ 20x + 25y = 7100 \quad \text{(2)} \]

### Step 3: Solve Equation (1) for \( y \)
From equation (1), we can express \( y \) in terms of \( x \):
\[ y = 324 - x \quad \text{(3)} \]

### Step 4: Substitute \( y \) in Equation (2)
Now, substitute equation (3) into equation (2):
\[ 20x + 25(324 - x) = 7100 \]
Expanding this gives:
\[ 20x + 8100 - 25x = 7100 \]

### Step 5: Combine Like Terms
Combine the \( x \) terms:
\[ -5x + 8100 = 7100 \]

### Step 6: Isolate \( x \)
Subtract 8100 from both sides:
\[ -5x = 7100 - 8100 \]
\[ -5x = -100 \]
Now, divide by -5:
\[ x = \frac{-100}{-5} = 20 \]

### Step 7: Calculate the Number of 25 Paise Coins
Using equation (3) to find \( y \):
\[ y = 324 - x = 324 - 20 = 304 \]

### Final Answer
The number of 20 paise coins is \( \boxed{20} \).