Question

a b and c share profit and losses in the ratio of 6 : 5: 3 d is admitted to into partnership for 1/8 share the sacrificing ratio of a : b : c is
1) 6: 5 : 3
2) 5: 4: 3
3) equal
4) none of these
​

Answer 1

Answer:

The Sacrificing Ratio :

Option 1) 6 : 5 : 3

a : b : c = 6 : 5 : 3

Explanation:

Solution :

★ Old Ratio :

a : b : c = 6 : 5 : 3

• a's Share = $\dfrac{6}{14}$

• b's Share = $\dfrac{5}{14}$

• c's Share = $\dfrac{3}{14}$

d is admitted to into partnership for 1/8 Share

Let,

Total profit Share = 1

• d's Share = $\dfrac{1}{8}$

Remaining Share =

$1 - \dfrac{1}{8} = \dfrac{7}{8}$

• a's New Share =

$\longrightarrow \: \dfrac{7}{8} \: \times \: \dfrac{6}{14}$

$\longrightarrow \: \dfrac{42}{112}$

• b's New Share =

$\longrightarrow \: \dfrac{7}{8} \: \times \: \dfrac{5}{14}$

$\longrightarrow \: \dfrac{35}{112}$

• c's New Share =

$\longrightarrow \: \dfrac{7}{8} \: \times \: \dfrac{3}{14}$

$\longrightarrow \: \dfrac{21}{112}$

• d's Share =

$\longrightarrow \: \dfrac{1}{8} \: = \: \dfrac{14}{112}$

★ New Profit Sharing Ratio :

• a : b : c : d

• $\dfrac{42}{112} : \dfrac{35}{112} : \dfrac{21}{112} : \dfrac{14}{112}$

★ The Sacrificing Ratio :

Sacrificing Ratio = Old Ratio - New Ratio

a's Sacrifice =

$\longrightarrow \: \dfrac{6}{14} \: - \: \dfrac{42}{112} \: = \: \dfrac{6}{112}$

b's Sacrifice =

$\longrightarrow \: \dfrac{5}{14} \: - \: \dfrac{35}{112} \: = \: \dfrac{5}{112}$

c's Sacrifice =

$\longrightarrow \: \dfrac{3}{14} \: - \: \dfrac{21}{112} \: = \: \dfrac{3}{112}$

The Sacrificing Ratio =

• a : b : c

• $\dfrac{6}{112} : \dfrac{5}{112} : \dfrac{3}{112}$

Therefore,

The Sacrificing Ratio :

Option 1) 6 : 5 : 3

a : b : c = 6 : 5 : 3

Answer 2

Answer:

Given :-

• a , b , c and d share profit and losses in the ratio of 6 : 5 : 3 is admitted to into partnership for ⅛ share.

To Find :-

• What is the sacrificing ratio of a : b : c.

Solution :-

First, we have to find the old ratio of a's , b's and c's share.

Given :

$\leadsto$ a : b : c = 6 : 5 : 3

Then,

$\mapsto$ Share of a's :

↦ $\sf \dfrac{6}{6 + 5 + 3}$

➦ $\sf\bold{\dfrac{6}{14}}$

$\mapsto$ Share of b's :

↦ $\sf \dfrac{5}{6 + 5 + 3}$

➦ $\sf\bold{\dfrac{5}{14}}$

$\mapsto$ Share of c's :

↦ $\sf \dfrac{3}{6 + 5 + 3}$

➦ $\sf\bold{\dfrac{3}{14}}$

Again, given that, d is admitted to into partnership for ⅛ share then,

Let, the total profit share of d's be 1

$\mapsto$ Share of d's :

↦ $\sf \dfrac{1}{8}$

$\longmapsto$ Remaining share of d's :

↦ $\sf 1 - \dfrac{1}{8}$

↦ $\sf \dfrac{8 - 1}{8}$

➦ $\sf\bold{\dfrac{7}{8}}$

Now, we have to find the new share of a's , b's , c's and d's.

$\mapsto$ New share of a's :

↛ $\sf \dfrac{6}{14} \times \dfrac{7}{8}$

↛ $\sf \dfrac{6 \times 7}{14 \times 8}$

➦ $\sf\bold{\dfrac{42}{112}}$

$\mapsto$ New share of b's :

↛ $\sf \dfrac{5}{14} \times \dfrac{7}{8}$

↛ $\sf \dfrac{5 \times 7}{14 \times 8}$

➦ $\sf\bold{\dfrac{35}{112}}$

$\mapsto$ New share of c's :

↛ $\sf \dfrac{3}{14} \times \dfrac{7}{8}$

↛ $\sf \dfrac{3 \times 7}{14 \times 8}$

➦ $\sf\bold{\dfrac{21}{112}}$

$\mapsto$ New share of d's :

↛ $\sf \dfrac{1}{8}$

➦ $\sf\bold{\dfrac{14}{112}}$

Now, as we know that,

$\bigstar \: \boxed{\sf{Sacrificing\: Ratio =\: Old\: Ratio -\: New\: Ratio}}$

$\mapsto$ Sacrificing Ratio of a's :

↦ $\sf \dfrac{6}{14} - \dfrac{42}{112}$

↦ $\sf \dfrac{48 - 42}{112}$

➦ $\sf\bold{\red{\dfrac{6}{112}}}$

$\mapsto$ Sacrificing Ratio of b's :

↦ $\sf \dfrac{5}{14} - \dfrac{35}{112}$

↦ $\sf \dfrac{40 - 35}{112}$

➦ $\sf\bold{\red{\dfrac{5}{112}}}$

$\mapsto$ Sacrificing Ratio of c's :

↦ $\sf \dfrac{3}{14} - \dfrac{21}{112}$

↦ $\sf \dfrac{24 - 21}{112}$

➦ $\sf\bold{\red{\dfrac{3}{112}}}$

Now, we have to find the sacrificing ratio :

$\implies$ $\sf a : b : c$

$\implies$ $\sf \dfrac{6}{\cancel{112}} : \dfrac{5}{\cancel{112}} : \dfrac{3}{\cancel{112}}$

$\implies$ $\sf\boxed{\bold{6 : 5 : 3}}$

Hence, the correct options is option no 1) 6 : 5 : 3.

$\therefore$ The sacrificing ratio of a : b : c is 6 : 5 : 3 .