‘P’ and ‘Q’ are partners, sharing profits in the ratio of 8 : 5 respectively. On 1st April 2016, they admitted R into partnership. The new profit sharing ratio among P, Q and R is fixed as 6 : 4 : 3 respectively. The sacrifice ratio of ‘P’ will be

$$rac{2}{{13}}$$
$$rac{1}{{13}}$$
$$rac{3}{{13}}$$
None of these

The correct answer is $\boxed{\frac{2}{13}}$.

The sacrifice ratio is the ratio in which the old partners give up their share of profit to the new partner.

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It is calculated by subtracting the new profit sharing ratio from the old profit sharing ratio. In this case, the old profit sharing ratio is 8:5 and the new profit sharing ratio is 6:4:3. Therefore, the sacrifice ratio of P is $\frac{8}{13} – \frac{6}{13} = \frac{2}{13}$.

Option A is incorrect because it is the old profit sharing ratio of P. Option B is incorrect because it is the new profit sharing ratio of P. Option C is incorrect because it is the sacrifice ratio of Q.

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