Question

A, B and C were partners in a firm sharing profits in 4 :3:2 ratio decided to share future profits in 4 : 3 : 1 ratio. Sacrificing ratio and gaining ratio will be​

Answer 1

Explanation:

★ Old Ratio :

A : B : C = 4 : 3 : 2

   $\sf{A's\:\:Share = \dfrac{4}{9}}$

   $\sf{B's\:\:Share = \dfrac{3}{9}}$

   $\sf{C's\:\:Share = \dfrac{2}{9}}$

They decided to share future profits in 4 : 3 : 1 ratio.

★ New Profit Sharing  Ratio :

A : B : C =  4 : 3 : 1

$\sf{A's\:new\:Share = \dfrac{4}{8}}$

$\sf{B's\:new\:Share = \dfrac{3}{8}}$

$\sf{C's\:new\:Share = \dfrac{1}{8}}$

★ Sacrificing Ratio or Gaining Ratio :

Sacrifice or Gain =  Old Ratio - New Ratio

• A =

$\longrightarrow{\sf{ \dfrac{4}{9} \: - \: \dfrac{4}{8} \: = \: \dfrac{(32 \: - \: 36)}{72}}}$

$\longrightarrow{\sf{\bold{\dfrac{( - \: 4)}{72} \: - - - - \: (GAIN)}}}$

_____________________________

• B =

$\longrightarrow{\sf{ \dfrac{3}{9} \: - \: \dfrac{3}{8} \: = \: \dfrac{(24 \: - \: 27)}{72}}}$

$\longrightarrow{\sf{\bold{\dfrac{( - \: 3)}{72} \: - - - - \: (GAIN)}}}$

_____________________________

• C =

$\longrightarrow{\sf{ \dfrac{2}{9} \: - \: \dfrac{1}{8} \: = \: \dfrac{(16 \: - \: 9)}{72}}}$

$\longrightarrow{\sf{\bold{\dfrac{7}{72} \: - - - - \: (SACRIFICE)}}}$

Therefore,

$\sf{A\:(Gain) = \dfrac{4}{72}}$

$\sf{B\:(Gain) = \dfrac{3}{72}}$

$\sf{C\:(Sacrifice) = \dfrac{7}{72}}$

Answer 2

Explanation:

old ratio of A,B and C = 4 :3:2

A = 4/9

B = 3/9

C = 2/9

new ratio :

A,B and C = 4 : 3 : 1

A = 4/8

B = 3/8

C = 1/8

Sacrifice or Gain : old ratio - new ratio

A = 4/9 - 4/8 = (32-36)/72

= -4/72 ---- Gain

B = 3/9 - 3/8 = (24-27)/72

= -3/72 ---- Gain

C = 2/9 - 1/8 = (16-9)/72

= 7/72 ---- Sacrifice

Hence , A gain = 4/72

B gain = 3/72

C Sacrifice = 7/72