Question

30. X and Y shared profit in ratio of 3 : 2. Z was admitted as a partner who gets 1/5th share New profit sharing ratio, if he acquires 3/20th from X and 1/20th from Y would be (a) 10:6:4 (b) 9:7:4 (c) 8:8:4 (d) 6:10:4 help me urgently
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Answer 1

Answer:

Option (b)

Explanation:

Solution :-

Given that

The ratio of the shares of the profits of X and Y = 3:2

Total parts of the profit of X and Y

= 3+2 = 5 parts

The share of X = Parts of X / Total Parts

= 3/5

The share of Y = Parts of Y / Total parts

= 2/5

Given that

Z was admitted as a partner with 1/5 th share

The share of the profit of Z = 1/5

If Z acquires 3/20 th from X then the new share of X = Old Share - Given share

= (3/5) - (3/20)

LCM of 5 and 20 = 20

= (12-3)/20

= 9/20

The new share of X = 9/20

If Z acquires 1/20 th from Y then the new share of Y = Old Share - Given share

= (2/5)-(1/20)

LCM of 5 and 20 = 20

= (8-1)/20

= 7/20

The new share of Y = 7/20

We have

X = 9/20 ,

Y = 7/20,

Z = 1/5 = (1/5)×(4/4) = (1×4)/(5×4) = 4/20

Now,

The new ratios of X,Y and Z

= (9/20) : (7/20) : (4/20)

= 9:7:4

Answer:-

The new ratio of the shares of the profit of X,Y and Z is 9:7:4

Answer 2

Answer:

Option (b) 9:7:4

Explanation:

Solution :

★ Old Ratio =

X : Y = 3 : 2

• X's Share = $\dfrac{3}{5}$

• Y's Share = $\dfrac{2}{5}$

Z was admitted as a partner who gets 1 /5 share.

Z acquires 3 /20 from X

Z acquires 1 / 20 from Y

★ New profit Sharing Ratio :

• X's New Share =

$\longrightarrow\: \dfrac{3}{5} \: - \: \dfrac{3}{20} \: = \: \dfrac{(12 \: - \: 3)}{20}$

$\longrightarrow\: \dfrac{9}{20}$

• Y's New Share =

$\longrightarrow\:\dfrac{2}{5} \: - \: \dfrac{1}{20} \: = \: \dfrac{(8 \: - \: 1)}{20}$

$\longrightarrow\: \dfrac{7}{20}$

• Z's Share =

$\longrightarrow\: \dfrac{1}{5} \: = \: \dfrac{4}{20}$

New profit Sharing Ratio :

• X : Y : Z

$\longrightarrow \: \dfrac{9}{20} : \dfrac{7}{20} : \dfrac{4}{20}$

$\longrightarrow$ 9 : 7 : 4

∴ Option (b) 9:7:4

New Profit Sharing Ratio = 9 : 7 : 4.