A total amount of Rs. 700 is divided among A, B and C such that A receives half as much as B, and B receives half as much as C. What is the share of C?

Introduction / Context:
This question checks your understanding of chained ratio relationships where each person's share is defined relative to another person. Instead of a direct ratio, we are given comparative statements, and we must convert them into an algebraic form to determine the individual shares from the total amount.

Given Data / Assumptions:

• Total amount shared by A, B and C is Rs. 700.
• A receives half as much as B, so A is smaller than B.
• B receives half as much as C, so B is smaller than C.
• We must calculate C's share.

Concept / Approach:
When one quantity is half of another, we can express both using a single variable. Here, the relations A = B / 2 and B = C / 2 allow us to express all three shares in terms of C. Once every share is written in terms of C, we can use the total sum equation A + B + C = 700 to solve for C directly.

Step-by-Step Solution:
Step 1: Let the share of C be C rupees. Step 2: B receives half as much as C, so B = C / 2. Step 3: A receives half as much as B, so A = B / 2 = (C / 2) / 2 = C / 4. Step 4: Total amount is A + B + C = 700. Step 5: Substitute A and B in terms of C: C / 4 + C / 2 + C = 700. Step 6: Convert the fractions to a common denominator of 4: C / 4 + 2C / 4 + 4C / 4 = 700. Step 7: Combine numerators: (1C + 2C + 4C) / 4 = 7C / 4 = 700. Step 8: Multiply both sides by 4: 7C = 700 * 4 = 2800. Step 9: Divide by 7: C = 2800 / 7 = 400. Step 10: Therefore, C's share is Rs. 400.

Verification / Alternative check:
With C = Rs. 400, B is half of C, so B = 400 / 2 = 200. A is half of B, so A = 200 / 2 = 100. Check the total: A + B + C = 100 + 200 + 400 = 700, which matches the given total amount. Both comparison conditions are satisfied, so the value for C is consistent and correct.

Why Other Options Are Wrong:
Rs. 200 and Rs. 300 do not satisfy the chain of half relationships when we back compute A and B, and they do not sum to Rs. 700 with the other derived shares.
Rs. 500 gives wrong totals and breaks the condition that B is half of C and A is half of B. Only Rs. 400 leads to a valid distribution of 100, 200 and 400 adding up to 700.

Common Pitfalls:
Students often reverse the relationships and treat C as half of B or B as half of A, which leads to incorrect equations. Another pitfall is to introduce unnecessary extra variables instead of expressing everything in terms of a single variable. Carefully reading the phrases "half as much as" and then converting them to clear equations helps to avoid confusion.

Final Answer:
The share of C is Rs. 400.