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 calculate the new profit-sharing ratio after admitting Kunal, we start with the existing ratio of Aman's and Riya's shares, which is 5:3. This means Aman has a share of \( \frac{5}{8} \) and Riya has \( \frac{3}{8} \) of the total profit.

Kunal is admitted with a \( \frac{1}{4} \) share, which he takes equally from Aman and Riya. Therefore, each of Aman and Riya's shares will be reduced by \( \frac{1}{8} \) (since \( \frac{1}{4} \div 2 = \frac{1}{8} \)).

Calculating the new shares:

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

Now, we need the new ratio. The fractions \(\frac{1}{2}\), \(\frac{1}{4}\), and \(\frac{1}{4}\) can be expressed with a common denominator, which is 4:

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

Thus, the new profit-sharing ratio of Aman, Riya, and Kunal is \(2:1:1\).