Amit and Vidya are partners sharing profits and losses

17 :- Amit and Vidya are partners sharing profits and losses in the ratio of 3:2. They admitted Chintan into partnership who acquires 1/5th of his share from Amit and 4/25th share from Vidya.
Calculate their new profit sharing ratio and sacrificing ratio.

Solution:-
Calculation of Chintan’s share in profit
Let the Chintan’s share be X
Chintan acquired 1//5th of his share from Amit = 1/5x
And he acquires flat 4/25th share from Vidya = 4/25
As per the given condition

1/5x + 4/25 = x
4/25 = x – 1/5x
4/25 = 4/5x
x = 4/25 x 5/4
x = 20/100
x = 1/5
Therefore, Chintan was admitted for 1/5th share

Calculation of New profit sharing ratio
Amit’s new share = 3/5 – (1/5 x 1/5) = 3/5 – 1/25 = 14/25
Vidya’s new share = 2/5 – 4/25 = 6/25
Chintan’s share = 1/5 x 5/5 = 5/25
Thus, New profit sharing ratio of Amit, Vidya and Chintan is 14:6:5

Calculation of sacrificing ratio of Amit and Vidya
Old share – new share
Amit = 3/5 – 14/25 = 1/25 (sacrifice)
Vidya = 2/5 – 6/25 = 4/25 (sacrifice)
Thus, sacrificing ratio of Amit and Vidya ia 1:4