Difficulty: Easy
Correct Answer: 3600
Explanation:
Introduction / Context:
This is a ratio and fraction distribution problem. A fixed amount of money is shared among three people A, B and C according to given fractions. We are told the exact amount received by C and the fractions for A and B. From this, we must compute A's share of the total amount.
Given Data / Assumptions:
Concept / Approach:
Let the total amount be T. Then the distribution conditions give:
A = T / 2, B = T / 3, C = 1200.
Since the whole amount is distributed, we have:
T/2 + T/3 + 1200 = T.
We solve this linear equation for T and then compute A = T/2. The key idea is to combine the fractions 1/2 and 1/3 correctly.
Step-by-Step Solution:
Step 1: Let total amount = T.
A's share = T/2; B's share = T/3; C's share = 1200.
Step 2: Set up the total distribution equation.
T/2 + T/3 + 1200 = T.
Step 3: Combine T/2 and T/3.
T/2 + T/3 = (3T + 2T) / 6 = 5T / 6.
So the equation becomes 5T/6 + 1200 = T.
Step 4: Move 5T/6 to the right-hand side.
1200 = T − 5T/6 = (1T/6) = T/6.
Step 5: Solve for T.
T/6 = 1200 → T = 1200 * 6 = 7200.
Step 6: Compute A's share.
A = T/2 = 7200 / 2 = 3600.
Verification / Alternative check:
Check B's and C's shares as well.
B = T/3 = 7200 / 3 = 2400.
C = 1200 (given).
Total distributed = 3600 + 2400 + 1200 = 7200, which matches T, so the distribution is correct.
Why Other Options Are Wrong:
If A received 4000, then B and C would together need to receive 3200, but 1/3 of the total would not match the given ₹ 1200 for C consistently.
Similarly, 1600, 1800 or 2400 for A would imply totals that are inconsistent with the fractions and with C's fixed amount of ₹ 1200.
Common Pitfalls:
Some students mistakenly add 1/2 and 1/3 as 2/5 instead of 5/6, which leads to an incorrect equation.
Others forget that C's amount must be included in the total along with A and B, incorrectly setting T/2 + T/3 = T.
Final Answer:
A receives ₹ 3600.
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