Question

Kumar, Lakshya, Manoj and Naresh are partners sharing profits in the ratio of 3: 2:14. Kumar retires and his share is acquired by Lakshya and Manoj in the ratio of 3:2. Calculate new profit sharing ratio and gaining ratio of the remaining partners New Ratio - 19: 11:20; Gaining Ratio - 3:2​

Answer 1

Answer:

K:L:M:N = 3:2:1:4

total share = 3+2+1+4= 10

kumar retires. kumar share = 3/10.

k's share is taken by L and M in 3:2 ratio. which means it is the gaining ratio .

CALCULATION OF NEW PROFIT RATIO of L:M:N

L takes 3/5 th share of K and M takes 2/5 th share of K.

L's share = 3/10 × 3/5 = 9/50

M's share= 3/10 × 2/5 = 6/50

L And M share already stood at 2/10 and 1/10 respectively. so adding old plus gaining we get

so L = 19/50

N = 11/50

N's share does not change . its 4/10. but we need to equal the denominator to get the new profit ratio. so 4/10× 5/5 = 20/50

so the new ratio becomes 19:11:20

Answer 2

Answer:

Explanation:

★ Appropriate Question :

Kumar, Lakshya, Manoj and Naresh are partners sharing profits in the ratio of 3: 2:1:4. Kumar retires and his share is acquired by Lakshya and Manoj in the ratio of 3:2. Calculate new profit sharing ratio and gaining ratio of the remaining partners New Ratio - 19: 11:20; Gaining Ratio - 3:2

Solution :

★ Old Ratio :

Kumar : Lakshya : Manoj : Naresh = 3 : 2 : 1 : 4

3 / 10 of Kumar's share acquired by Lakshya and Manoj

$\sf{Lakshya \: acquired \: share \: = \dfrac{3}{10} \times \dfrac{3}{5} = \dfrac{9}{50}}$

$\sf{Manoj \: acquired \: share \: = \dfrac{3}{10} \times \dfrac{2}{5} = \dfrac{6}{50}}$

$\sf{Lakshya \:new \: share \: = \: \dfrac{2}{10} + \dfrac{9}{50} = \dfrac{(10 \: + \: 9)}{50}}$

$\sf{Lakshya \:new \: share \: = \: \dfrac{19}{50}}$

$\sf{Manoj \: new \: share \: = \dfrac{1}{10} + \dfrac{6}{50} = \dfrac{(5 \: + \: 6)}{50}}$

$\sf{Manoj \: new \: share \: = \dfrac{11}{50}}$

$\sf{Naresh \: share = \: \dfrac{4}{10} \: \times \: \dfrac{5}{5}}= \dfrac{20}{50}$

The new profit sharing ratio =

$\sf{Lakshya \: :\:Manoj\: :\:Naresh\:= \dfrac{19}{50}} : \: \dfrac{11}{50}\::\dfrac{20}{50}$

Lakshya : Manoj : Naresh = 19 : 11 : 20

The new profit sharing ratio between Lakshya, Manoj and Naresh will be 19 : 11 : 20

★ Gaining Ratio = New Ratio - Old Ratio

$\sf{Lakshya \: = \: \dfrac{19}{50} - \dfrac{2}{10} = \dfrac{19\:-\:10}{50}}$

$\sf{Lakshya \: = \: \dfrac{9}{50}}$

$\sf{Manoj \: = \: \dfrac{11}{50} - \dfrac{1}{10} =\dfrac{11\:-\:5}{50}}$

$\sf{Manoj \: = \: \dfrac{6}{50}}$

Gaining Ratio =

$\sf{Lakshya \: :\:Manoj\: = \dfrac{9}{50}} : \: \dfrac{6}{50}$

9 : 6 = 3 : 2

Therefore,

New Ratio - 19: 11:20 and Gaining Ratio - 3:2