Question

P,Q and R share profit and losses in the ration of $4:3:2$ respectively. Q retires and P and R decided to share future profits and losses in the ratio of $5:3$. Then immediately H is admitted of $3/10$ shares of profits half of which was gifted by P an remaining shares was taken by H equally form P and R. Calculate the new profit sharing ratio after H' admission and gain ratio of P and R.

• A. New profit sharing ratio = $4:3:3$ and Gain Ratio = $13:11$
• B. New profit sharing ratio = $3:3:4$ and Gain Ratio = $11:13$
• C. New profit sharing ratio = $4:4:3$ and Gain Ratio = $13:11$
• D. New profit sharing ratio = $5:3:2$ and Gain Ratio = $11:13$

Answer 1

The correct option is A New profit sharing ratio = $4:3:3$ and Gain Ratio = $13:11$

Old ratio (P, Q and R) = 4 : 3 : 2

New Ratio (P and R) = 5 : 3

Gaining ratio = New ratio - Old ratio

P's gain = (5/8) - (4/9) = 13/72

R's gain = (3/8) - (2/9) = 11/72

On H's admission :

Old ratio (P and R) = 5 : 3

H is admitted for 3/10 shares

P's sacrifice in favour of H = (3/10) * (3/4) = 9/40 .............(1/2 + 1/4 = 3/4)

R's sacrifice in favour of H = (3/10) * (1/4) = 3/40

New ratio = Old ratio - sacrificing ratio

P's new share = (5/8) - (9/40) = 16/40

R's new share = (3/8) - (3/40) = 12/40

H's share = P's sacrifice + R's sacrifice

= (9/40) + (3/40)

= 12/40

Therefore, new ratio of P, R and H is 16 : 12 : 12 or 4 : 3 : 3