A and B start a business with capitals in the ratio 5:3. After 6 months, A withdraws ₹10,000 and B doubles his investment. If the initial investment of A was ₹50,000, and the total profit after 1 year is ₹84,000, find the profit share of A.

Correct — A. Find B's capital, then add capital × months over the two halves of the year.

B's capital: 50,000 × 3⁄5 = 30,000

A: 50,000 × 6 + (50,000 − 10,000) × 6
= 3,00,000 + 2,40,000 = 5,40,000

B: 30,000 × 6 + (2 × 30,000) × 6
= 1,80,000 + 3,60,000 = 5,40,000

Ratio 1 : 1, so A's share = 84,000 ÷ 2 = ₹42,000 → option (a)

Why the others are wrong

• (b)
  ₹50,000 — ₹50,000 is A's starting capital, not a profit share. It is also more than half of ₹84,000, which would need A's capital × months to exceed B's, and the two are equal.
• (c)
  ₹60,000 — ₹60,000 is B's capital after doubling, a figure from the working, not A's share. A's 5,40,000 equals B's 5,40,000, so A gets ₹42,000.
• (d)
  ₹45,000 — ₹45,000 would need A : B = 15 : 13. The half-year products give 5,40,000 each, a 1 : 1 split, so A's share is ₹42,000.

When capital changes partway, split the year at the change and add capital × months for each piece. A partner's total is the sum of those pieces.

Here the change comes at 6 months. A drops from 50,000 to 40,000 while B rises from 30,000 to 60,000. The ratio 5 : 3 describes the starting capitals, so it is used once, to find B's 30,000, and never to split the profit.

Key facts

• Capitals 5 : 3 with A = ₹50,000 give B = 50,000 × 3⁄5 = ₹30,000.
• A: 50,000 × 6 + 40,000 × 6 = 5,40,000 rupee-months.
• B: 30,000 × 6 + 60,000 × 6 = 5,40,000 rupee-months.

Common traps

• Splitting the profit 5 : 3 by the starting capitals, which gives A ₹52,500.
• Applying the ₹10,000 withdrawal to the full year instead of only the last 6 months.

No directly related past PYQ was found.