‘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. 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.