X started a business with ₹93,750, and after some months, Y joined with…
2026
X started a business with ₹93,750, and after some months, Y joined with ₹75,000. At the end of the year, the profit was divided between X and Y in the ratio 5 : 3. After how many months from the start did Y join the business?
Answer: B. 3 — ConceptIn a partnership, each partner’s share of profit is proportional to capital × time for which that capital remains invested. If one partner joins after…
- A.
9
- B.
3
- C.
5
- D.
4
Attempted by 17 students.
Show answer & explanation
Correct answer: B
Concept
In a partnership, each partner’s share of profit is proportional to capital × time for which that capital remains invested.
If one partner joins after d months in a 12-month year, that partner’s investment period is 12 − d months.
Application
Let Y’s investment remain in the business for t months. X invests for the full 12 months.
Therefore, X : Y profit share = (93,750 × 12) : (75,000 × t) = 5 : 3.
Cross-multiplying gives 3 × 93,750 × 12 = 5 × 75,000 × t.
Hence t = (3 × 93,750 × 12) ÷ (5 × 75,000) = 9 months.
Y therefore joined after 12 − 9 = 3 months from the start.
Cross-check
With Y investing for 9 months, the capital-time ratio is (93,750 × 12) : (75,000 × 9) = 1,125,000 : 675,000 = 5 : 3, which matches the stated profit ratio.
Thus, Y joined the business 3 months after X started it.