Question

1. X Y and Z are partners sharing profits and losses in the ratio of 5 : 3:2. They admit A into partnership
and give him 1/5th share of profits. Find the new profit-sharing ratio.
​

Answer 1

Answer:

New profit-Sharing Ratio =

• X : Y : Z : A
• 10 : 6 : 4 : 5

Explanation:

Old Ratio :

X : Y : Z = 5 : 3 : 2

• X's Share = $\dfrac{5}{10}$

• Y's Share = $\dfrac{3}{10}$

• Z's Share = $\dfrac{2}{10}$

★ They admit A into partnership and give him 1 / 5 th share of profits

Let,

Total Profit Share = 1

So,

• A's Share = $\dfrac{1}{5}$

Remaining Share :

$1 - \dfrac{1}{5} = \dfrac{4}{5}$

• X's New Share =

$\longrightarrow \: \dfrac{4}{5} \: \times \: \dfrac{5}{10}$

$\longrightarrow \: \dfrac{20}{50}$

• Y's New Share =

$\longrightarrow \: \dfrac{4}{5} \: \times \: \dfrac{3}{10}$

$\longrightarrow \: \dfrac{12}{50}$

• Z's New Share =

$\longrightarrow \: \dfrac{4}{5} \: \times \: \dfrac{2}{10}$

$\longrightarrow \: \dfrac{8}{50}$

• A's Share =

$\longrightarrow \: \dfrac{1}{5} \: = \: \dfrac{10}{50}$

★ New profit-Sharing Ratio =

• X : Y : Z : A

• $\dfrac{20}{50} : \dfrac{12}{50} : \dfrac{8}{50} : \dfrac{10}{50}$

$\longrightarrow$ 20 : 12 : 8 : 10

$\longrightarrow$ 10 : 6 : 4 : 5

Therefore,

New profit-Sharing Ratio =

• X : Y : Z : A
• 10 : 6 : 4 : 5

Answer 2

Answer:

Given :-

• X , Y and Z are partners sharing profits and losses in the ratio of 5 : 3 : 2. They admit A into partnership and give him ⅕th share of profits.

To Find :-

• What is the new ratio of profit sharing.

Solution :-

First, we have to find the share of X's , Y's and Z's.

$\longmapsto$ Share of X's :

↦ $\sf \dfrac{5}{5 + 3 + 2}$

➦ $\sf\bold{\pink{\dfrac{5}{10}}}$

$\longmapsto$ Share of Y's :

↦ $\sf \dfrac{3}{5 + 3 + 2}$

➦ $\sf\bold{\pink{\dfrac{3}{10}}}$

$\longmapsto$ Share of Z's :

↦ $\sf \dfrac{2}{5 + 3 + 2}$

➦ $\sf\bold{\pink{\dfrac{2}{10}}}$

Again, they admit A into partnership and give him ⅕th share of profits.

Let, the total share of profits of A's be 1

Then, the share of A's :

➦ $\sf\bold{\pink{\dfrac{1}{5}}}$

And, the remaining share of A's :

↦ $\sf 1 - \dfrac{1}{5}$

↦ $\sf \dfrac{5 - 1}{5}$

➦ $\sf\bold{\pink{\dfrac{4}{5}}}$

Now, we have to find the new share of X's , Y's , Z's and A's :

$\mapsto$ New share of X's :

↦ $\sf \dfrac{5}{10} \times \dfrac{4}{5}$

↦ $\sf \dfrac{5 \times 4}{10 \times 5}$

➠ $\sf\bold{\red{\dfrac{20}{50}}}$

$\mapsto$ New share of Y's :

↦ $\sf \dfrac{3}{10} \times \dfrac{4}{5}$

↦ $\sf \dfrac{3 \times 4}{10 \times 5}$

➠ $\sf\bold{\red{\dfrac{12}{50}}}$

$\mapsto$ New share of Z's :

↦ $\sf \dfrac{2}{10} \times \dfrac{4}{5}$

↦ $\sf \dfrac{2 \times 4}{10 \times 5}$

➠ $\sf\bold{\red{\dfrac{8}{50}}}$

$\mapsto$ New share of A's :

↦ $\sf \dfrac{1}{5}$

➠ $\sf\bold{\red{\dfrac{10}{50}}}$

Now, we have to find the new profit-sharing ratio :

⇒ $\sf X : Y : Z : A$

⇒ $\sf \dfrac{20}{\cancel{50}} : \dfrac{12}{\cancel{50}} : \dfrac{8}{\cancel{50}} : \dfrac{10}{\cancel{50}}$

⇒ $\sf 20 : 12 : 8 : 10$

➲ $\sf\boxed{\bold{10 : 6 : 4 : 5}}$

$\therefore$ The new profit-sharing ratio is 10 : 6 : 4 : 5 .