Three friends X, Y and Z started a business by investing sums of money in the…
2026
Three friends X, Y and Z started a business by investing sums of money in the ratio 5 : 2 : 8. After 6 months, X withdraws half of his capital. If the sum invested by Z is ₹19000, then out of a total annual profit of ₹55000, what is the difference between X's and Y's profit?
Answer: A. ₹7000 — Concept: In a partnership the annual profit is divided in the ratio of each partner's capital multiplied by the time that capital stayed in the business — the…
- A.
₹7000
- B.
₹6195
- C.
₹7355
- D.
₹8405
Attempted by 13 students.
Show answer & explanation
Correct answer: A
Concept: In a partnership the annual profit is divided in the ratio of each partner's capital multiplied by the time that capital stayed in the business — the capital-months. The capitals alone give the same ratio whenever every partner keeps his money in for the whole of the same period, because that common time factor cancels out. Once a partner's capital changes part-way through the period, or the partners invest for unequal lengths of time, only the capital-months give the correct split.
So whenever a partner's capital changes part-way through the year, split that partner's year into periods, multiply each capital by the length of its own period, and add those products to get a single capital-months figure for that partner.
Application: Let the three investments be 5k, 2k and 8k. X holds 5k for the first 6 months and, after withdrawing half, holds 2.5k for the remaining 6 months, while Y and Z hold their capital for all 12 months.
Partner | Capital × time | Capital-months |
|---|---|---|
X | 5k × 6 + 2.5k × 6 | 45k |
Y | 2k × 12 | 24k |
Z | 8k × 12 | 96k |
Profit-sharing ratio = 45k : 24k : 96k = 15 : 8 : 32, after dividing every term by 3k.
Total number of parts = 15 + 8 + 32 = 55.
Value of one part = ₹55000 ÷ 55 = ₹1000.
X's profit = 15 × ₹1000 = ₹15000, and Y's profit = 8 × ₹1000 = ₹8000.
Cross-check: ₹15000 + ₹8000 + ₹32000 (Z's 32 parts) = ₹55000, exactly the whole annual profit, so the division is consistent. The gap can also be read straight off the parts: 15 − 8 = 7 parts, that is 7 × ₹1000.
Why ₹19000 is not needed: Z's actual investment only fixes the size of one part of capital, ₹19000 ÷ 8 = ₹2375 (so X put in ₹11875 and Y ₹4750). The capital-months still come out in the ratio 15 : 8 : 32, and a profit share depends only on that ratio, so the answer does not change.
Answer: The difference between X's and Y's profit is ₹7000.