P, Q and R have been sharing profits and losses in the ratio of `5:3:2`. Q retires. His share is taken by P and R in the ratio of `2:1`. New profit sharing ratio will be:
Answers
Explanation:
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
Explanation:
Solution :
★ Old Ratio :
P : Q : R = 5:3:2
- P's share = 5/10
- Q's share = 3/10
- R's share = 2/10
Q retires,
Q's share is taken by P and R in the ratio of 2:1.
Q's share taken by P =
3/10 × 2/3 = 6/30
Q's share taken by R =
3/10 × 1/3 = 3/30
★ New profit sharing ratio :
• P's new share =
5/10 + 6/30 = (15 + 6)/30
21/30
• R's new share =
2/10 + 3/30 = (6 + 3)/30
9/30
New profit sharing ratio =
- P : R
- 21/30 : 9/30
- 21 : 9
7 : 3
Therefore, New profit sharing ratio will be 7 : 3.