A person has only ₹1 and ₹2 coins. The total number of coins is 50 and the total amount is ₹75. Find the number of ₹1 coins and ₹2 coins, respectively.

Introduction / Context:
Classic coin-count problems involve two variables: the number of lower-denomination coins and higher-denomination coins. You are given both the total count of coins and the total monetary value, which leads to a solvable system of linear equations.

Given Data / Assumptions:

• Total coins = 50.
• Total value = ₹75.
• Only denominations used are ₹1 and ₹2 coins.

Concept / Approach:
Let x be the count of ₹1 coins and y be the count of ₹2 coins. Then x + y = 50 (count equation) and x + 2y = 75 (value equation). Solve simultaneously to get x and y in integers consistent with the constraints.

Step-by-Step Solution:

Verification / Alternative check:
Total amount = 25*₹1 + 25*₹2 = 25 + 50 = ₹75; total coins = 25 + 25 = 50. Both conditions satisfied.

Why Other Options Are Wrong:

• 15 and 35; 35 and 15; 30 and 20; 20 and 30: Each pair violates either the total coin count of 50 or the total value of ₹75 when tested.

Common Pitfalls:

• Mistakenly using 2x + y = 75 instead of x + 2y = 75 (mixing denominations).
• Not checking that both equations are satisfied simultaneously.

Final Answer:
25 and 25