Question

a, b and c were partners in a firm sharing profits in the ratio of 3:2:1. they admitted d as a new partner for 1/8th share in the profits, calculate sacrificing ratio of a, b, c will be: a. 1:1:1. b. 2:1:1. c. 3:2:1. d. 4:3:2​

Answer 1

Answer:

(C) 3:2:1

Explanation:

OLD RATIO OF A,B&C IS 3:2:1 ⇒ 3/6:2/6:1/6

D'S AGREED SHARE IS 1/8

ASSUMING THAT TOTAL SHARE IS 1

REMANING SHARE = 1-1/8 = 7/8

NEW RATIO OF A,B,C&D IS

A' SHARE = 3/6*7/8=21/48

B'S SHARE = 2/6*7/8=14/48

C'S SHARE = 1/6*7/8 = 7/48

D'S SHARE = 1/8*6/6 = 6/48

NEW RATIO OF A,B,C&D IS 21:14:7:6

SACRIFICING RATIO = OLD-NEW

 A'S SACRIFICE = 3/6-21/48=3/48

B'S SACRIFICE = 2/6-14/48=2/48

C'S SACRIFICE = 1/6-7/48=1/48

SACRIFICING RATIO OF A,B&C = A:B:C=3:2:1

Answer 2

ANSWER :

❖ Option (C) 3 : 2 : 1

• ✎ If A, B and C were partners in a firm sharing profits in the ratio of 3 : 2 : 1 and D was admitted as a new partner for 1/8 th share in the profits; then the Sacrificing Ratio of A, B and C will be 3 : 2 : 1.

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SOLUTION :

❒ Given :-

• A, B and C were partners in a firm sharing profits in the ratio of 3 : 2 : 1.

• D was admitted as a new partner for $\rm{\dfrac{1}{8}}$ th share in the profits.

❒ To Calculate :-

• Sacrificing Ratio of A, B and C = ?

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❒ Working Note :-

It is given that,

• D was admitted as a new partner for $\rm{\dfrac{1}{8}}$ th share in the profits.

Let us suppose,

• Total profit of the firm = 1

So,

• ✠ Share of C = $\bf{\dfrac{1}{8}}$ th of 1

⇥ Share of C = $\bf{\dfrac{1}{8} \times 1}$

⇥ Share of C = $\bf{\dfrac{1}{8}}$

Then,

• ⍟ Remaining Share = $\rm{1 - \dfrac{1}{8}}$ th

➞ Remaining Share = $\rm{\dfrac{8 - 1}{8}}$ th

➞ Remaining Share = $\rm{\dfrac{7}{8}}$ th

Again,

• A, B and C were partners in a firm sharing profits in the ratio of 3 : 2 : 1.

So,

• Old Share of A = $\sf{\dfrac{3}{6}}$

• Old Share of B = $\sf{\dfrac{2}{6}}$

• Old Share of C = $\sf{\dfrac{1}{6}}$

Now,

• The remaining $\rm{\dfrac{7}{8}}$ th share of profit will be shared by A, B and C in the ratio of 3 : 2 : 1.

So,

• ❍ New Share of A = $\sf{\dfrac{3}{6}}$ of $\tt{\dfrac{7}{8}}$

⇒ New Share of A = $\sf{\dfrac{3}{6} \times \dfrac{7}{8}}$

⇒ New Share of A = $\sf{\dfrac{21}{48}}$

And,

• ❍ New Share of B = $\sf{\dfrac{2}{6}}$ of $\tt{\dfrac{7}{8}}$

⇒ New Share of B = $\sf{\dfrac{2}{6} \times \dfrac{7}{8}}$

⇒ New Share of B = $\sf{\dfrac{14}{48}}$

Also,

• ❍ New Share of C = $\sf{\dfrac{1}{6}}$ of $\tt{\dfrac{7}{8}}$

⇒ New Share of C = $\sf{\dfrac{1}{6} \times \dfrac{7}{8}}$

⇒ New Share of C = $\sf{\dfrac{7}{48}}$

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❒ Calculation :-

We have,

• Old Share of A = $\tt{\dfrac{3}{6}}$

• Old Share of B = $\tt{\dfrac{2}{6}}$

• Old Share of C = $\tt{\dfrac{1}{6}}$

And,

• New Share of A = $\tt{\dfrac{21}{48}}$

• New Share of B = $\tt{\dfrac{14}{48}}$

• New Share of C = $\tt{\dfrac{7}{48}}$

We know that,

• $\dag \: \: \underline{ \boxed{ \bold{ \: Sacrifice = Old \: \: Share- New \: \: Share \: }}}$

Using this formula, we get,

• ⊚ Sacrifice of A = Old Share of A - New Share of A

➜ Sacrifice of A = $\tt{\dfrac{3}{6} - \dfrac{21}{48}}$

➜ Sacrifice of A = $\tt{\dfrac{24 - 21}{48}}$

➜ Sacrifice of A = $\tt{\dfrac{3}{48}}$

Similarly,

• ⊚ Sacrifice of B = Old Share of B - New Share of B

➜ Sacrifice of B = $\tt{\dfrac{2}{6} - \dfrac{14}{48}}$

➜ Sacrifice of B = $\tt{\dfrac{16 - 14}{48}}$

➜ Sacrifice of B = $\tt{\dfrac{2}{48}}$

And,

• ⊚ Sacrifice of C = Old Share of C - New Share of C

➜ Sacrifice of C = $\tt{\dfrac{1}{6} - \dfrac{7}{48}}$

➜ Sacrifice of C = $\tt{\dfrac{8 - 7}{48}}$

➜ Sacrifice of C = $\tt{\dfrac{1}{48}}$

Hence,

• ✪ Sacrificing Ratio of A, B and C = Sacrifice of A : Sacrifice of B : Sacrifice of C

➨ Sacrificing Ratio of A, B and C = $\tt{\dfrac{3}{48}}$ : $\tt{\dfrac{3}{48}}$ : $\tt{\dfrac{1}{48}}$

∴ Sacrificing Ratio of A, B and C = 3 : 2 : 1