Coin-mix linear equations: 324 coins (20p and 25p) total Rs. 71 – find count of 25p coins

Introduction / Context:
Mixed-coin problems are standard linear equation applications. Here, two denominations add to a known count and a known total value. The goal is to solve for the number of higher-value coins.

Given Data / Assumptions:

• Total coins = 324.
• Denominations: 20 paise and 25 paise.
• Total value = Rs. 71 = 7100 paise.

Concept / Approach:
Let x be the count of 25p coins and y be the count of 20p coins. Translate the two constraints—total pieces and total value—into equations, then solve.

Step-by-Step Solution:

Verification / Alternative check:
Then y = 324 − 124 = 200 coins of 20p. Value check: 12425 + 20020 = 3100 + 4000 = 7100 paise (Rs. 71). Correct.

Why Other Options Are Wrong:

• 120, 144, 200: None satisfy both the piece-count and value equations simultaneously.

Common Pitfalls:
Forgetting to convert rupees to paise, or mixing x and y when substituting back into equations.

Final Answer:
124