Aman, Naman and Neel were partners in a firm sharing profits in the ratio of 1 : 2 : 1. Neel retires and he surrenders 2/3rd of his share in favour of Aman and the remaining share... Aman, Naman and Neel were partners in a firm sharing profits in the ratio of 1 : 2 : 1. Neel retires and he surrenders 2/3rd of his share in favour of Aman and the remaining share in favour of Naman. Calculate the new profit sharing ratio of Aman and Naman.
Understand the Problem
The question is asking to calculate the new profit-sharing ratio after one partner, Neel, retires and surrenders part of his share in favor of another partner, Naman. This involves understanding the initial sharing ratio and adjusting it based on the changes caused by Neel's retirement.
Answer
$5 : 7$
Answer for screen readers
The new profit-sharing ratio of Aman and Naman is $5 : 7$.
Steps to Solve
- Understand the initial profit-sharing ratio
The initial profit-sharing ratio among Aman, Naman, and Neel is given as $1:2:1$. This means Aman's share is $1x$, Naman's share is $2x$, and Neel's share is $1x$.
- Calculate Neel's share to be surrendered
Since Neel is surrendering $\frac{2}{3}$ of his share, we first find Neel's total share, which is $1x$. Thus, the amount he surrenders is:
$$ \text{Surrendered share} = \frac{2}{3} \times 1x = \frac{2}{3}x $$
- Determine the remaining share of Neel
The remaining share after surrendering part of it will be:
$$ \text{Remaining share of Neel} = 1x - \frac{2}{3}x = \frac{1}{3}x $$
- Distribute the surrendered share
Neel surrenders his surrendered share in favor of Aman and Naman. The problem states that Aman receives $\frac{2}{3}$ of the surrendered share, and Naman receives the remaining part of the surrendered share.
- Aman's new share:
$$ \text{Aman's new share} = 1x + \frac{2}{3}x = \frac{3}{3}x + \frac{2}{3}x = \frac{5}{3}x $$
- Naman's share is increased by the remaining part of Neel's surrendered share. Naman receives $\frac{1}{3}$ of Neel's surrendered share (because Aman receives $\frac{2}{3}$):
$$ \text{Naman's new share} = 2x + \frac{1}{3}x $$
To simplify, we convert $2x$ to have a common denominator of 3:
$$ 2x = \frac{6}{3}x $$
Thus,
$$ \text{Naman's new share} = \frac{6}{3}x + \frac{1}{3}x = \frac{7}{3}x $$
- Write the new profit-sharing ratio
The new profit-sharing ratio of Aman and Naman can now be expressed as follows:
- Aman's share: $ \frac{5}{3}x $
- Naman's share: $ \frac{7}{3}x $
The new ratio is:
$$ \text{New Ratio} = \frac{5}{3} : \frac{7}{3} = 5 : 7 $$
The new profit-sharing ratio of Aman and Naman is $5 : 7$.
More Information
The new profit-sharing ratio indicates how profits will be divided among the remaining partners after Neel's retirement. This change is essential for understanding how to calculate shares in a partnership.
Tips
- Misunderstanding the shares: Students might confuse the initial shares, so it's important to correctly assign shares before and after the changes.
- Not converting to a common denominator: When calculating the total shares for new ratios, failing to have a common denominator can lead to incorrect additions.
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