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

Question

Accepted Answer

To determine the number of 20 paise coins, we need to solve the problem using the given information:

1. **Total number of coins**: 324 coins
2. **Total value of coins**: ₹71, which is equivalent to 7100 paise (since 1 rupee = 100 paise)

Let the number of 20 paise coins be $ x $. Then, the number of 25 paise coins will be $ 324 - x $.

The total value of the coins can be expressed as:
$$ 20x + 25(324 - x) = 7100 $$

Simplifying this equation:
$$ 20x + 8100 - 25x = 7100 $$
$$ -5x + 8100 = 7100 $$
$$ -5x = 7100 - 8100 $$
$$ -5x = -1000 $$
$$ x = 200 $$

Thus, the number of 20 paise coins is 200, which corresponds to Option 3.

**Explanation for why other options are incorrect:**

- **Option 1 (124 coins)**: If there were 124 coins of 20 paise, the equation would be:
  $$ 20(124) + 25(324 - 124) = 2480 + 5000 = 7480 \text{ paise} $$
  This does not equal 7100 paise, so this option is incorrect.

- **Option 2 (140 coins)**: If there were 140 coins of 20 paise, the equation would be:
  $$ 20(140) + 25(324 - 140) = 2800 + 4600 = 7400 \text{ paise} $$
  This also does not equal 7100 paise, so this option is incorrect.

- **Option 4 (210 coins)**: If there were 210 coins of 20 paise, the equation would be:
  $$ 20(210) + 25(324 - 210) = 4200 + 2850 = 7050 \text{ paise} $$
  This does not equal 7100 paise, so this option is incorrect.

Therefore, the correct answer is Option 3, with 200 coins of 20 paise.