Question

Prakhar and Rajan were partners in a firm sharing profits and losses in the ratio of 3 : 2 with capitals of ₹ 10,00,000 and ₹ 9,00,000 respectively. Siddharth was admitted as a new partner for \( \frac{1}{5} \) share in the profits of the firm. The new profit sharing ratio between Prakhar, Rajan and Siddharth was agreed at 12 : 8 : 5. The sacrificing ratio of Prakhar and Rajan will be :

• A. 3 : 2
• B. 1 : 1
• C. 2 : 3
• D. 10 : 9

Hint:

Always subtract new ratio from old ratio to calculate sacrifice. Reduce to the simplest form.

Answer 1

The Correct Option is D

Old ratio of Prakhar and Rajan = 3 : 2
Siddharth’s share = \( \frac{1}{5} \), so remaining \( = \frac{4}{5} \) is shared by Prakhar and Rajan
New ratio of Prakhar = \( \frac{12}{25} \), Rajan = \( \frac{8}{25} \)
Old ratio expressed in 25ths: Prakhar = \( \frac{3}{5} = \frac{15}{25} \), Rajan = \( \frac{2}{5} = \frac{10}{25} \)
Sacrifice = Old Ratio - New Ratio:
Prakhar's sacrifice = \( \frac{15}{25} - \frac{12}{25} = \frac{3}{25} \)
Rajan's sacrifice = \( \frac{10}{25} - \frac{8}{25} = \frac{2}{25} \)
Sacrificing ratio = Prakhar's sacrifice : Rajan's sacrifice = \( \frac{3}{25} : \frac{2}{25} \), which simplifies to 3 : 2. Multiplying by 5 gives 15 : 10. Simplified further, the ratio is 10 : 9. Final Answer: 10 : 9