P, Q, and R start a business. Twice P's capital equals thrice Q's capital, and Q's capital is four times R's capital. If the annual profit is ₹ 1,48,500, what is Q's share?

Introduction / Context:
Translating chained relationships into a single ratio for three partners enables proportional profit sharing.

Given Data / Assumptions:

• 2P = 3Q ⇒ P : Q = 3 : 2.
• Q = 4R ⇒ Q : R = 4 : 1.
• Annual profit = ₹ 1,48,500.

Concept / Approach:
Combine ratios so that all three are expressed together. Then use the total parts to find each share.

Step-by-Step Solution:
From 2P = 3Q, P : Q = 3 : 2. From Q : R = 4 : 1, let Q = 4k ⇒ P = (3/2)*Q = 6k and R = 1k. Thus P : Q : R = 6 : 4 : 1 (equivalent to 3 : 2 : 0.5 scaled by 2). Total parts = 6 + 4 + 1 = 11. Q's fraction = 4/11. Q's share = (4/11) * 1,48,500 = ₹ 54,000.

Verification / Alternative check:
Remaining profit for P and R sums to 7/11 of 1,48,500 = ₹ 94,500, consistent with the partition.

Why Other Options Are Wrong:
They correspond to incorrect combined ratios or arithmetic with the fraction 4/11.

Common Pitfalls:
Writing P : Q as 2 : 3 or missing the step to link Q with R correctly.

Final Answer:
₹ 54,000