X and Y are the partners sharing profit and loss in the ratio of 3:2 . they admit Z with 1 /7th share in profit . calculate the new ratio and sacrifice ratio .
Answers
Answer: New ratio of partners is 18 : 12 : 7 and Sacrifice Ratio is 3 : 2.
Step by step explanation:
Given that, Old ratio of X and Y = 3 : 2.
Z is admitted for 1/7th share of profit.
We know that,
Balance of 1 = 1 - share of new partner
= 1 - 1/7
= 6/7 [...remaining share]
Now,
New ratio = Old ratio × balance of 1
X's new ratio = 3/5 × 6/7
= 18/35
Y's new ratio = 2/5 × 6/7
= 12/35
Z's new ratio = 1/7 or 7/35 ..[given]
Thus, New ratio of partners = 18/35 : 12/35 : 7/35 or 18 : 12 : 7.
Finding out sacrifice ratio,
Sacrifice ratio = Old ratio - new ratio
X's Sacrifice Ratio = 3/5 - 18/35
= (21 - 18)/ 35
= 3/35
Y's Sacrifice Ratio = 2/5 - 12/35
= (14 - 12)/35
= 2/35
Thus, Sacrifice Ratio = 3/35 : 2/35 or 3 : 2.
Given :-
X and Y are the partners sharing profit and loss in the ratio of 3:2 . they admit Z with 1 /7th share in profit .
To Find :-
New Ratio
Sacrifice Ratio
Solution :-
At first we need to find the new ratio to calculate sacrifice ratio
Total part in old ratio = 3 + 2 = 5
Old ratio of X = 3/5
Old ratio of Y = 2/5
They Admit Z with 1/7 share of profit. This means Z have 1/7 part of total share
Total Share = 1
Share for X and Y = 1 - 1/7
Share for X and Y = 7 - 1/7
Share for X and Y = 6/7
Now
New Ratio (X) = 3/5 × 6/7
New Ratio (X) = 18/35
New Ratio (Y) = 2/5 × 6/7
New Ratio (Y) = 12/35
New Ratio (Z) = 1/7
Now,
Finding Sacrifice Ratio for X and Y
For X = 3/5 - 18/35
⇒ 21 - 18/35
⇒ 3/35
For Y = 2/5 - 12/35
⇒ 14 - 12/35
⇒ 2/35
Ratio = 3:2