A certain amount of money is fully distributed among A, B and C in such a way that A receives 1/2 of the total amount, B receives 1/3 of the total amount and C receives Rs 1200. How much money does A receive?

Introduction / Context:
This question involves sharing an amount of money according to given fractional parts. It tests your ability to work with fractions of a whole and to reconstruct the total from one person's share.

Given Data / Assumptions:
- The total amount of money is completely distributed among A, B and C.
- A receives 1/2 of the total amount.
- B receives 1/3 of the total amount.
- C receives Rs 1200.
- We must find A's share.

Concept / Approach:
Let the total amount be T. Then A receives T / 2, B receives T / 3 and C receives the remaining amount. Since the full amount is distributed, the sum of their shares equals T. This allows us to express C's share as a fraction of T, then equate it to Rs 1200 and solve for T. After that we compute A's share as T / 2.

Step-by-Step Solution:
Step 1: Let the total amount be T. Step 2: A's share = T / 2, B's share = T / 3. Step 3: Total distributed = T / 2 + T / 3 + C's share = T. Step 4: Combine A and B shares: T / 2 + T / 3 = (3T + 2T) / 6 = 5T / 6. Step 5: Therefore, C's share is T - 5T / 6 = T / 6. Step 6: We are told C receives Rs 1200, so T / 6 = 1200. Step 7: Multiply both sides by 6: T = 1200 * 6 = 7200. Step 8: A's share = T / 2 = 7200 / 2 = 3600.

Verification / Alternative check:
Check B's share as well: B receives 1/3 of 7200, which is 2400. A receives 3600, B receives 2400, and C receives 1200. Their sum is 3600 + 2400 + 1200 = 7200, which matches the total T, so the distribution is consistent.

Why Other Options Are Wrong:
- Option 4000: This would give a total greater than 7200 when combined with correct shares for B and C.

- Option 1600: This is less than C's share, which contradicts the fact that A receives the largest fraction.

- Option 1800: This would imply a much smaller total, inconsistent with C receiving 1200 as only one sixth of the total.

Common Pitfalls:
Some learners add the fractions 1/2 and 1/3 incorrectly or forget that the remaining share belongs entirely to C. Others do not recognise that the full distribution implies 1/2 + 1/3 + C's fraction = 1. Always convert the known shares to fractions of the total and ensure they sum to 1.

Final Answer:
A receives 3600 rupees.