A and B invest ₹45,000 and ₹60,000 respectively. A remains in business for 8 months, B for 6 months. If the total profit is ₹36,000, what is A’s share?
- (a)₹16,000
- (b)₹18,000
- (c)₹20,000
- (d)₹24,000
Answer
Why
Correct — B. Profit is shared in the ratio of capital × months.
A: 45,000 × 8 = 3,60,000
B: 60,000 × 6 = 3,60,000
Ratio A : B = 1 : 1
A's share = 36,000 ÷ 2 = ₹18,000 → option (b)
Why the others are wrong
- (a)₹16,000 — ₹16,000 leaves B ₹20,000, a 4 : 5 split. The capital-months are equal, 3,60,000 each, so the profit splits 1 : 1.
- (c)₹20,000 — ₹20,000 leaves B ₹16,000, a 5 : 4 split in A's favour. Neither partner has more capital-months, so neither gets the larger share.
- (d)₹24,000 — ₹24,000 leaves B ₹12,000, a 2 : 1 split. That would need A's capital × months to be double B's, but both are 3,60,000.
Concept
In a partnership, profit is shared in proportion to capital × time, the capital-months each partner puts in.
A larger sum for a shorter time can match a smaller sum for a longer time. A's smaller capital stays 8 months and B's larger one only 6, and the products come out equal, so the profit splits evenly.
Reducing first avoids big numbers: 45 : 60 = 3 : 4 and 8 : 6 = 4 : 3, so the profit ratio is 3 × 4 : 4 × 3 = 12 : 12 = 1 : 1.
Key facts
- Profit ratio = ratio of each partner's capital × months.
- Partners with equal capital × months share the profit equally.
- A partner's share = total profit × own capital-months ÷ total capital-months.
Study next
Common traps
- Splitting by capital alone, 3 : 4, or by time alone, 4 : 3. Profit follows the product of the two.
- Giving A the larger share because A stayed longer, without weighing B's larger capital.
14 Sep 2025, 16:00, Quant Q.4 balances the same way: 25,000 × 12 = 50,000 × 6, so A takes half of ₹30,000, ₹15,000.
12 Sep 2025, 09:00, Quant Q.6 does too: 80,000 × 9 = 1,20,000 × 6, so B's share is half of ₹45,000, ₹22,500.
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