Ninad, Vikas and Manav enter into a partnership. Ninad invests some amount at…
2023
Ninad, Vikas and Manav enter into a partnership. Ninad invests some amount at the beginning. Vikas invests double the amount after 6 months and Manav invests thrice the amount invested by Ninad after 8 months. They earn a profit of Rs 45,000 at the end of the year. What is Manav's share in the profit ?
- A.
Rs 25,000
- B.
Rs 15,000
- C.
Rs 12,000
- D.
Rs 9,000
Show answer & explanation
Correct answer: B
In a partnership where partners invest different amounts of capital for different lengths of time, the profit is shared in the ratio of each partner's capital multiplied by the time for which it stayed invested (Capital × Time), not just the ratio of the capital amounts themselves.
Applying this to the given partnership:
Ninad invests Rs x right from the start of the year, so his capital works for the full 12 months. His capital-time value = x × 12 = 12x.
Vikas invests Rs 2x, joining 6 months into the year, so his capital works for the remaining 12 − 6 = 6 months. His capital-time value = 2x × 6 = 12x.
Manav invests Rs 3x, joining 8 months into the year, so his capital works for the remaining 12 − 8 = 4 months. His capital-time value = 3x × 4 = 12x.
Comparing the three capital-time values gives Ninad : Vikas : Manav = 12x : 12x : 12x = 1 : 1 : 1, so the total profit of Rs 45,000 is split equally three ways. Manav's share = 45,000 ÷ 3 = Rs 15,000.
Cross-check: If each partner receives Rs 15,000, the three shares add up to 15,000 + 15,000 + 15,000 = Rs 45,000, which matches the total profit stated in the question, confirming the equal 1 : 1 : 1 split.