In a partnership, A invests ₹6,000 for 9 months and B invests ₹8,000 for some…
2023
In a partnership, A invests ₹6,000 for 9 months and B invests ₹8,000 for some months. Their profits are ₹1,800 and ₹1,600 respectively. For how many months did B invest?
Answer: C. 6 months — ConceptIn a partnership, profit is divided in the ratio of each partner’s capital-time product. If a partner invests capital C for time t, the effective…
- A.
4 months
- B.
5 months
- C.
6 months
- D.
8 months
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept
In a partnership, profit is divided in the ratio of each partner’s capital-time product.
If a partner invests capital C for time t, the effective investment is C × t; therefore, profit ratio = capital-time ratio.
Application
Let B invest for x months. A’s capital-time product is 6,000 × 9 = 54,000 month-rupees, while B’s is 8,000x month-rupees.
The profit ratio is 1,800 : 1,600 = 9 : 8.
Equate the capital-time ratio to the profit ratio: 54,000 : 8,000x = 9 : 8.
Cross-multiplication gives 54,000 × 8 = 9 × 8,000x, so 432,000 = 72,000x and x = 6.
Cross-check
For 6 months, B’s capital-time product is 8,000 × 6 = 48,000. Thus A : B = 54,000 : 48,000 = 9 : 8, the same as 1,800 : 1,600.
Result
B invested for 6 months.