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Answer:
★ Appropriate Question :
X,Y and Z are partners in a firm sharing profits and losses in the raio of 5:3:2. Y retires from the firm and his share was taken up by X and Z in the ratio of 2:1. Calculate the new profit sharing ratio.
Answer :
The New Profit Sharing Ratio = X : Z = 7 : 3
Explanation:
Solution :
Old Ratio :
X : Y : Z = 5 : 3 : 2
X's Share = \dfrac{5}{10}
10
5
Y's Share = \dfrac{3}{10}
10
3
Z's Share = \dfrac{2}{10}
10
2
Y retires from the firm.
His share was taken up by X and Z in the ratio of 2 : 1.
Y's Share = \dfrac{3}{10}
10
3
• Y's Share taken by X =
\longrightarrow \: \dfrac{3}{10} \: \times \: \dfrac{2}{3} \: = \: \dfrac{6}{30}⟶
10
3
×
3
2
=
30
6
\longrightarrow \: \dfrac{6}{30} \: = \: \dfrac{2}{10}⟶
30
6
=
10
2
• Y's Share taken by Z =
\longrightarrow \: \dfrac{3}{10} \: \times \: \dfrac{1}{3} \: = \: \dfrac{3}{30}⟶
10
3
×
3
1
=
30
3
\longrightarrow \: \dfrac{3}{30} \: = \: \dfrac{1}{10}⟶
30
3
=
10
1
★ The New Profit Sharing Ratio :
• X's New Share =
\longrightarrow\: \dfrac{5}{10} \: + \dfrac{2}{10}⟶
10
5
+
10
2
\longrightarrow \: \dfrac{7}{10}⟶
10
7
• Z's New Share =
\longrightarrow \: \dfrac{2}{10} \: + \: \dfrac{1}{10}⟶
10
2
+
10
1
\longrightarrow \: \dfrac{3}{10}⟶
10
3
The New Profit Sharing Ratio :
X : Z
\longrightarrow \: \dfrac{7}{10}\::\dfrac{3}{10}⟶
10
7
:
10
3
\longrightarrow⟶ 7 : 3
Therefore, The New Profit Sharing Ratio = X : Z = 7 : 3