Rs. 700 is to be divided among A, B, and C such that A gets half of B’s share and B gets half of C’s share. What is C’s share?

Introduction / Context:
This division problem relates the three shares by simple fractions. By expressing all shares in terms of C, the total can be solved quickly.

Given Data / Assumptions:

• A = 1/2 of B.
• B = 1/2 of C.
• Total A + B + C = Rs. 700.

Concept / Approach:
Express B and A in terms of C to compute the sum: C + C/2 + C/4. Then equate to 700 and solve for C.

Step-by-Step Solution:
B = C/2; A = B/2 = C/4. Sum = C + C/2 + C/4 = (4C + 2C + C)/4 = 7C/4. 7C/4 = 700 ⇒ 7C = 2800 ⇒ C = 400.

Verification / Alternative check:
Then B = 200 and A = 100. Total = 100 + 200 + 400 = 700, consistent with the condition A = 1/2 B and B = 1/2 C.

Why Other Options Are Wrong:
Rs. 200 or Rs. 300 do not satisfy the fractional relationships. Rs. 600 would overshoot the total when combined with A and B.

Common Pitfalls:
Confusing “half as much as” with “twice as much as”, or not expressing all terms consistently in terms of a single variable.

Final Answer:
Rs. 400