Naveen, Suresh and Tarun are partners sharing profits and losses in the ratio of 5:3:2. Suresh retires from the firm and his share was acquired by Naveen and Tarun in the ratio 2:1. What will be the new profits and losses sharing ratio of Naveen and Tarun ?

Question

Accepted Answer

The correct option is 4: 7:3

This question requires the calculation of the new profit-sharing ratio upon the retirement of a partner, which is a core topic in Partnership Accounts. The underlying concept is that the retiring partner's share of profit must be acquired by the remaining partners, increasing their respective shares. The original profit-sharing ratio of Naveen (N), Suresh (S), and Tarun (T) is 5:3:2, meaning Suresh's share is 3/10 of the total profit. The key piece of information is that the remaining partners, Naveen and Tarun, acquired this 3/10 share in the ratio of 2:1. To find the new ratio, we first calculate the exact gain for each continuing partner. Naveen gains $(3/10) 	imes (2/3) = 2/10$, and Tarun gains $(3/10) 	imes (1/3) = 1/10$. We then add this gained share to their respective old shares. Naveen's new share is his old share of $5/10$ plus his gain of $2/10$, resulting in $7/10$. Tarun's new share is his old share of $2/10$ plus his gain of $1/10$, resulting in $3/10$. Therefore, the new profit-sharing ratio between Naveen and Tarun is $7/10 : 3/10$, which simplifies to $7:3$.

The incorrect option is 1: 8:2
This option is incorrect because it implies that Naveen gained $3/10$ and Tarun gained zero, or that the ratio was calculated using an incorrect base. If Naveen's new share was $8/10$, his gain would have been $3/10$ ($8/10 - 5/10$), leaving Tarun's share unchanged at $2/10$. However, the problem explicitly states that Suresh's share was acquired by both Naveen and Tarun in the ratio of $2:1$. The total of 8:2 also sums to 10, but the distribution of Suresh's share is fundamentally wrong here.

The incorrect option is 2: 4:7
This ratio is arithmetically impossible for the partners' shares, as the sum of the ratio parts (4 + 7 = 11) does not correspond to a common denominator that would result from the given old shares and gains. Specifically, Naveen's old share was $5/10$, which is already $50%$ of the profit, making a new share of $4/11$ (less than $5/10$) illogical when a partner is gaining. A retiring partner's share is always distributed to the continuing partners, meaning their shares must increase, not decrease. This ratio would also suggest Tarun's share increased dramatically more than Naveen's, which contradicts the $2:1$ gaining ratio.

The incorrect option is 3: 7:4
This option, summing to 11, incorrectly attempts to calculate the new ratio by potentially adding the old share's numerator and the gained portion's denominator or using the gaining ratio incorrectly. Naveen's correct new share is $7/10$. If the ratio were $7:4$, Tarun's share would be $4/11$, which is much higher than his correct new share of $3/10$. This suggests a mathematical error, likely in calculating Tarun's gained share or his final share. Both partners' shares must be calculated using the common denominator of 10 for the final ratio to be accurate, which is $7:3$ or $7/10 : 3/10$.