'A', 'B', and 'C' formed a consulting firm. Their capital investments were Rs. 6,00,000, Rs. 4,00,000, and Rs. 5,00,000, respectively. After 3 months, 'A' withdrew Rs. 1,00,000, and 'B' added Rs. 1,00,000. The partnership lasted for 9 months. What was the ratio of their effective capital contributions?

Correct — A. Effective capital = amount × months it stayed in, counted in lakh-months.

A: 6 × 3 + 5 × 6 = 18 + 30 = 48
B: 4 × 3 + 5 × 6 = 12 + 30 = 42
C: 5 × 9 = 45

Ratio 48 : 42 : 45. Divide by 3 → 16 : 14 : 15 → option (a)

Why the others are wrong

• (b)
  16:15:14 — 16 : 15 : 14 swaps B and C. B's 42 lakh-months is below C's 45, because B held only 4 lakh for the first three months.
• (c)
  14:15:16 — 14 : 15 : 16 gives A the smallest share, but A's 48 lakh-months is the largest. Even after the withdrawal A still held 5 lakh, as much as C.
• (d)
  14:16:15 — 14 : 16 : 15 swaps A and B. A starts at 6 lakh and falls to 5, while B starts at 4 and rises to 5, so A's total is higher.

When capital changes part-way, profit is shared in the ratio of capital × time, added up over each period.

Split the 9 months at the change: months 1–3 at the old amounts, months 4–9 at the new ones.

From month 4 all three partners hold 5 lakh. So the whole difference in the ratio comes from the first three months, when they held 6, 4 and 5 lakh.

Key facts

• Profit ratio = ratio of the sum of (capital × months) for each partner.
• Working in lakhs keeps the numbers small: ₹6,00,000 for 3 months counts as 6 × 3 = 18.
• A withdrawal lowers the capital from that month on, and an addition raises it.

Common traps

• Using the new amounts for all 9 months, which gives 5 : 5 : 5.
• Writing the right numbers in the wrong order. The options differ only in order, so match A, B and C to 48, 42 and 45 one by one.

No directly related past PYQ was found.