Question

A and b were partners sharing profit and loss in 3: 2 they admit 'c' as a ne patner their new profit sharing ratio 12:8:5 find out the sacrifice ratio of A&B​

Answer 1

Explanation:

★ Old Ratio :

A : B = 3 : 2

• A's Share = 3/5
• B's Share = 2/5

They admit C as a new partner.

★ New Profit Sharing Ratio =

A : B : C = 12:8:5

• A's new share= 12/25
• B's new share = 8/25
• C's new share = 5/25

★ Sacrificing Ratio = Old Ratio - New Ratio

A = 3/5 - 12/25

⇒ (15 - 12)/25 = 3/25

B = 2/5 - 8/25

⇒ (10 - 8)/25 = 2/25

Sacrificing Ratio =

A : B = 3/25 : 2/25

⇒ 3 : 2

Therefore, the sacrifice ratio of A&B = 3:2.

Answer 2

Answer:

Given :-

• A & B were partners sharing profit and loss in 3 : 2 they admitted C as a new partner, their new profit sharing ratio is 12 : 8 : 5.

To Find :-

• What is the sacrifice ratio of A & B.

Solution :-

First, we have to find the old ratio of A & B :

$\leadsto \sf Old\: Ratio =\: A : B$

$\leadsto \bf{Old\: Ratio =\: 3 : 2}$

Hence, the old ratio of A & B will be :

❒ Old Ratio of A :

$\implies \sf Old\: Ratio\: of\: A =\: \dfrac{3}{3 + 2}$

$\implies \sf\bold{\green{Old\: Ratio\: of\: A =\: \dfrac{3}{5}}}$

❒ Old Ratio of B :

$\implies \sf Old\: Ratio\: of\: B =\: \dfrac{2}{3 + 2}$

$\implies \sf\bold{\green{Old\: Ratio =\: \dfrac{2}{5}}}$

$\bigstar$ They admitted C as a new partner.

Now, we have to find the new profit sharing ratio of A & B :

$\implies \sf New\: Sharing\: Profit\: Ratio =\: A : B : C$

$\implies \bf{New\: Sharing\: Profit\: Ratio =\: 12 : 8 : 5}$

❒ New Ratio Of A :

$\implies \sf New\: Ratio\: of\: A =\: \dfrac{12}{12 + 8 + 5}$

$\implies \sf New\: Ratio\: of\: A =\: \dfrac{12}{20 + 5}$

$\implies \sf\bold{\green{New\: Ratio\: of\: A =\: \dfrac{12}{25}}}$

❒ New Ratio Of B :

$\implies \sf New\: Ratio\: of\: B =\: \dfrac{8}{12 + 8 + 5}$

$\implies \sf New\: Ratio\: of\: B =\: \dfrac{8}{20 + 5}$

$\implies \sf\bold{\green{New\: Ratio\: of\: B =\: \dfrac{8}{25}}}$

❒ New Ratio Of C :

$\implies \sf New\: Ratio\: of\: C =\: \dfrac{5}{12 + 8 + 5}$

$\implies \sf New\: Ratio\: of\: C =\: \dfrac{5}{20 + 5}$

$\implies \sf\bold{\green{New\: Ratio\: of\: C =\: \dfrac{5}{25}}}$

Now, we have to find the sacrificing ratio of A & B :

As we know that :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Sacrificing\: Ratio =\: Old\: Ratio - New\: Ratio}}}$

➦ A's Sacrifice :

$\implies \sf A's\: Sacrifice =\: \dfrac{3}{5} - \dfrac{12}{25}$

$\implies \sf A's\: Sacrifice =\: \dfrac{15 - 12}{25}$

$\implies \sf\bold{\purple{A's\: Sacrifice =\: \dfrac{3}{25}}}$

➦ B's Sacrifice :

$\implies \sf B's\: Sacrifice =\: \dfrac{2}{5} - \dfrac{8}{25}$

$\implies \sf B's\: Sacrifice =\: \dfrac{10 - 8}{25}$

$\implies \sf\bold{\purple{B's\: Sacrifice =\: \dfrac{2}{25}}}$

Hence, the sacrifice ratio of A & B :

$\longrightarrow \bf Sacrifice\: Ratio =\: A : B$

$\longrightarrow \sf Sacrifice\: Ratio =\: \dfrac{3}{25} : \dfrac{2}{25}$

$\longrightarrow \sf\bold{\red{Sacrifice\: Ratio =\: 3 : 2}}$

${\small{\bold{\underline{\therefore\: The\: sacrifice\: ratio\: of\: A\: \&\: B\: is\: 3 : 2\: .}}}}$