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
  % OCR interpretation might be slightly off, checking logic. Calculation: Ishan gets 4/10 * 1/2 = 2/10. Kapil gets 4/10 * 1/2 = 2/10. New Ishan = 5/10 + 2/10 = 7/10. New Kapil = 1/10 + 2/10 = 3/10. Ratio 7:3. OK.

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

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).