P and Q are partners sharing profits in the ratio of 2 : 1. They admitted R into partnership giving him $\frac{1}{5}$th share which he acquired from P and Q in 1 : 2 ratio. Calculate the new profit sharing ratio.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) - 3 : 1 : 1.
Old ratio = 2:1 (P & Q)
R admit with 1/5th share
Sacrificing ratio = 1:2
P sacrifice = 1/5 x 1/3
= 1/15
Q sacrifice = 1/5 x 2/3
= 2/15
New share = Old share- sacrifice share
New share of P = 2/3 - 1/15
= (10-1)15
= 9/15
New share of Q = 1/3 - 2/15
= (5 -2)/15
= 3/15
NEW RATIO = 9/15 : 3/15 :1/5
= 9/15 : 3/15 : 3/15
= 9 :3:3
= 3:1:1