Question

3. A, B, C and D are partners sharing profits in equal proportions. They decide to share the profits in
the ratio of 5:4:3:2 in future. You are required to calculate sacrificing ratios and the gaining
ratios for the partners.
​

Answer 1

Answer:

old ratio = a,b,c,d is 1234

Answer 2

Answer:

A Gain = $\sf{\dfrac{3}{28}}$

B Gain =$\sf{\dfrac{1}{28}}$

C Sacrifice = $\sf{\dfrac{1}{28}}$

D Sacrifice = $\sf{\dfrac{3}{28}}$

Explanation:

Given :

• A, B, C and D are partners sharing profits in equal proportions

• They decide to share the profits in the ratio of 5:4:3:2 in future.

To find : Calculate Sacrificing ratios and the Gaining ratios for the partners

Solution :

Old Ratio ( A : B : C : D) =

⇒ $\sf{\dfrac{1}{4} : \dfrac{1}{4} :\dfrac{1}{4} :\dfrac{1}{4}}$

New Ratio = 5 : 4 : 3 : 2

⇒ $\sf{\dfrac{5}{14} : \dfrac{4}{14} : \dfrac{3}{14} : \dfrac{2}{14}}$

★ Calculations Of Sacrifice or Gain Share of Partners :

Sacrificing Share = Old Share - New Share

• A =

⇒ $\sf{\dfrac{1}{4} - \dfrac{5}{14} \: = \dfrac{7 \: - \: 10}{28}}$

⇒ $\sf{\dfrac{7 \: - \: 10}{28} = ( - ) \dfrac{3}{28} ---- (Gain)}$

• B =

⇒ $\sf{\dfrac{1}{4} - \dfrac{4}{14} = \dfrac{7 \: - \: 8}{28}}$

⇒ $\sf{\dfrac{7 \: - \: 8}{28} = ( - ) \dfrac{ 1}{28} ---- (Gain)}$

• C =

⇒ $\sf{\dfrac{1}{4} - \dfrac{3}{14} = \dfrac{7 \: - \: 6}{28}}$

⇒ $\sf{\dfrac{7 \: - \: 6}{28} \: = \dfrac{1}{28} ---- (Sacrifice)}$

• D =

⇒ $\sf{\dfrac{1}{4} - \dfrac{2}{14} = \dfrac{7 \: - \: 4}{28}}$

⇒ $\sf{\dfrac{7 \: - \: 4}{28} = \dfrac{3}{28} ---- (Sacrifice)}$

Therefore,

A Gain = $\sf{\dfrac{3}{28}}$

B Gain =$\sf{\dfrac{1}{28}}$

C Sacrifice = $\sf{\dfrac{1}{28}}$

D Sacrifice = $\sf{\dfrac{3}{28}}$