Question

Aman and Riya share profits in the ratio 5:3. They admitted Kunal for \(\frac{1}{4}\) share, which he took equally from both. Calculate the new ratio.

• A. \(2:1:1\)
• B. \(9:7:4\)
• C. \(10:6:3\)
• D. \(5:3:2\)

Hint:

When a new partner is admitted by taking equal shares from existing partners, subtract the shares equally and find the new ratio by expressing all shares as fractions of the total.

Answer 1

The Correct Option is A

To determine the updated profit-sharing ratio subsequent to Kunal's admission, we commence with the pre-existing ratio between Aman and Riya, which is 5:3. This establishes Aman's share as \( \frac{5}{8} \) and Riya's share as \( \frac{3}{8} \) of the total profit.

Kunal is admitted with a \( \frac{1}{4} \) share, sourced equally from Aman and Riya. Consequently, both Aman's and Riya's individual shares will be reduced by \( \frac{1}{8} \), derived from \( \frac{1}{4} \div 2 = \frac{1}{8} \).

The calculation of the revised shares is as follows:

• Aman's revised share: \( \frac{5}{8} - \frac{1}{8} = \frac{4}{8} = \frac{1}{2} \)
• Riya's revised share: \( \frac{3}{8} - \frac{1}{8} = \frac{2}{8} = \frac{1}{4} \)
• Kunal's share: \( \frac{1}{4} \)

To ascertain the new ratio, we express the fractions \(\frac{1}{2}\), \(\frac{1}{4}\), and \(\frac{1}{4}\) with a common denominator of 4:

• Aman's share: \( \frac{2}{4} \)
• Riya's share: \( \frac{1}{4} \)
• Kunal's share: \( \frac{1}{4} \)

Therefore, the new profit-sharing ratio among Aman, Riya, and Kunal is established as \(2:1:1\).