Question

(Ans ! 3.2.1)
2. A,B,C were partners in a firm sharing profits in 3:2:1 ratio. They admitted D for
10% profits. Calculate the new profit sharing ratio?
(Ans : 9:6:3:2)​

Answer 1

Explanation:

Old ratio =

A:B:C = 3:2:1

A = 3/6

B = 2/6

C = 1/6

They admitted D for 10% profit

consider,

firm's total Profit = 1

D's share = 10%

=> 10/100 = 1/10

remaining share =

1 - 1/10 = 9/10

The new profit sharing ratio

=> A = 9/10 × 3/6 = 27/60

=> B = 9/10 × 2/6 = 18/60

=> C = 9/10 × 1/6 = 9/60

=> D = 1/10 = 6/10

The new profit sharing ratio

A:B:C:D =

=> 27/60 : 18/60 : 9/20 : 6/20

=> 27 : 18 : 9 : 6 = 9 : 6 : 3 : 2

.°. The new profit sharing ratio of A,B,C and D =

9 : 6 : 3 : 2

Answer 2

ANSWER :

• ❖ If A,B,C were partners in a firm sharing profits in 3 : 2 : 1 ratio and they admitted D for 10% profits; then the new profit sharing ratio of A, B, C and D will be 9 : 6 : 3 : 2.

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SOLUTION :

❒ Given :-

• Profit sharing ratio of A, B, C partners = 3 : 2 : 1

• D was admitted for 10% profit.

❒ To Calculate :-

• New profit sharing ratio of A, B, C and D = ?

❒ Calculation :-

It is given that,

• Profit sharing ratio of A, B, C partners is 3 : 2 : 1

Thus,

• A's share of profit = $\sf{\dfrac{3}{6}}$

• B's share of profit = $\sf{\dfrac{2}{6}}$

• C's share of profit = $\sf{\dfrac{1}{6}}$

Again,

• D was admitted in the firm for 10% profits.

Let us suppose,

• The total profit of the firm = 1

Then,

• D's share of profit = 10% of 1

➜ D's share of profit = $\sf{\dfrac{10}{100}}$ × 1

➜ D's share of profit = $\sf{\dfrac{1}{10}}$

• ∴ Remaining share = 1 - $\sf{\dfrac{1}{10}}$

➜ Remaining share = $\sf{\dfrac{10 - 1 }{10}}$

➜ Remaining share = $\sf{\dfrac{9}{10 }}$

• ⥀ This remainging share of $\sf{\dfrac{9}{10}}$ will be shared by A, B and C in their old ratio, i.e, 3 : 2 : 1.

So,

• ★ The new share of A = $\sf{\dfrac{3}{6}}$ of $\sf{\dfrac{9}{10}}$

➨ The new share of A = $\sf{\dfrac{3}{6}}$ × $\sf{\dfrac{9}{10}}$

➨ The new share of A = $\sf{\dfrac{9}{20}}$

• ★ The new share of B = $\sf{\dfrac{2}{6}}$ of $\sf{\dfrac{9}{10}}$

➨ The new share of B = $\sf{\dfrac{2}{6}}$ × $\sf{\dfrac{9}{10}}$

➨ The new share of B = $\sf{\dfrac{6}{20}}$

• ★ The new share of C = $\sf{\dfrac{1}{6}}$ of $\sf{\dfrac{9}{10}}$

➨ The new share of C = $\sf{\dfrac{1}{6}}$ × $\sf{\dfrac{9}{10}}$

➨ The new share of C = $\sf{\dfrac{3}{20}}$

And,

• ★ The share of D = $\sf{\dfrac{1}{10}}$

➨ The share of D = $\sf{\dfrac{1 \times 2}{10 \times 2}}$

➨ The share of D = $\sf{\dfrac{2}{20}}$

• ∴ New profit sharing ratio = $\sf{\dfrac{9}{20}}$ : $\sf{\dfrac{6}{20}}$ : $\sf{\dfrac{3}{20}}$ : $\sf{\dfrac{2}{20}}$

➩ New profit sharing ratio = 9 : 6: 3 : 2

• ✎ Hence, the new profit sharing ratio of A, B, C and D is 9 : 6: 3 : 2.