Question

Ishan, Jatin and Kapil were partners in a firm sharing profits and losses in the ratio of 5:4:1. Jatin retired and his share was taken up by Ishan and Kapil in the ratio 1:1. The new profit-sharing ratio between Ishan and Kapil after Jatin's retirement will be:

• A. 5:1
• B. 1:1
• C. 5:4
• D. 7:3

Hint:

When a retiring partner's share is taken by remaining partners in a specific ratio, first calculate the actual fraction of profit gained by each remaining partner. Then, add this gained share to their respective old shares to find the new profit-sharing ratio. New Share = Old Share + Gained Share.

Answer 1

The Correct Option is D

To determine the new profit-sharing ratio between Ishan and Kapil after Jatin's retirement, follow these steps:

1. Initially, the profit-sharing ratio among Ishan, Jatin, and Kapil is 5:4:1.
2. Jatin's share is 4/10 of the total.
3. Upon Jatin's retirement, his share of 4/10 is taken by Ishan and Kapil in the given ratio of 1:1. This means each takes half of Jatin's share.
4. Calculate Ishan's new share:
   • Original share: 5/10
   • Additional from Jatin: 2/10
   • Total new share: 5/10 + 2/10 = 7/10
5. Calculate Kapil's new share:
   • Original share: 1/10
   • Additional from Jatin: 2/10
   • Total new share: 1/10 + 2/10 = 3/10
6. The new profit-sharing ratio between Ishan and Kapil is therefore 7:3.

Answer 2

Old Ratio (Ishan : Jatin : Kapil) = 5:4:1 (\( \frac{5}{10} : \frac{4}{10} : \frac{1}{10} \)) Jatin retires. His share was \( \frac{4}{10} \). Jatin's share is taken by Ishan and Kapil in the ratio 1:1. Share gained by Ishan = Jatin's Share \( \times \) Ishan's proportion of gain \[ \text{Ishan's Gain} = \frac{4}{10} \times \frac{1}{2} = \frac{4}{20} = \frac{2}{10} \] Share gained by Kapil = Jatin's Share \( \times \) Kapil's proportion of gain \[ \text{Kapil's Gain} = \frac{4}{10} \times \frac{1}{2} = \frac{4}{20} = \frac{2}{10} \] New Share = Old Share + Gained Share Ishan's New Share = \( \frac{5}{10} + \frac{2}{10} = \frac{7}{10} \) Kapil's New Share = \( \frac{1}{10} + \frac{2}{10} = \frac{3}{10} \) The new profit-sharing ratio between Ishan and Kapil is 7:3. This matches Option (D).