A started a software business by investing ₹21000. After three months, B…
2026
A started a software business by investing ₹21000. After three months, B joined him with a capital of ₹32000. After 4 years, they earned a profit of ₹40800. What was A's share (in ₹, rounded off to the nearest integer) in the profit?
Answer: C. 16800 — Concept: In a partnership, profit is never divided by capital alone or by time alone. It is divided in the ratio of each partner's capital multiplied by time…
- A.
16704
- B.
16732
- C.
16800
- D.
16746
Attempted by 17 students.
Show answer & explanation
Correct answer: C
Concept: In a partnership, profit is never divided by capital alone or by time alone. It is divided in the ratio of each partner's capital multiplied by time — the money a partner puts in, multiplied by the number of months it stays in the business.
For two partners, the profit is shared in the ratio of their capital-and-time products:
C1t1 : C2t2
Applying it here:
Partner | Capital (₹) | Months invested | Capital × Months |
|---|---|---|---|
A | 21000 | 48 | 10,08,000 |
B | 32000 | 45 | 14,40,000 |
The business runs for 4 years, that is 4 × 12 = 48 months, and A's ₹21000 stays in it for all 48 months.
B joins three months after the start, so B's ₹32000 stays in the business for 48 − 3 = 45 months.
A's capital × time = 21000 × 48 = 10,08,000.
B's capital × time = 32000 × 45 = 14,40,000.
Profit-sharing ratio = 10,08,000 : 14,40,000 = 1008 : 1440 = 7 : 10, dividing both terms by 144.
Total parts = 7 + 10 = 17, so one part of the profit = 40800 ÷ 17 = ₹2,400.
A's share = 7 × ₹2,400 = ₹16,800.
Cross-check: B's share is 10 × ₹2,400 = ₹24,000, and ₹16,800 + ₹24,000 = ₹40,800, which is the whole profit, so the split is consistent. As a fraction A receives 7/17, about 41.18% of the profit — exactly A's weight in the combined capital-months. The division is exact, so the instruction to round off to the nearest integer changes nothing here.
Common trap: Splitting the profit in the ratio of the capitals alone, 21000 : 32000 = 21 : 32, ignores that B's money worked for three fewer months. Time must be weighted in before the ratio is formed.