Question

A &b share profits in the ratio of 2:1 .C is admitted with 1/4 share in profits.C acquires 3/4 of his share from A and 1/4 of his share from B. the new ratio will be?

Answer 1

Answer:

Given :-

• A and B share profit in the ratio of 2 : 1. C is admitted with ¼ share in profits. C acquires ¾ of his share from A and ¼ of his share from B.

To Find :-

• What is the new ratio of A, B and C.

Solution :-

Given :

$\mapsto$ Share of A = $\sf \dfrac{2}{3}$

$\mapsto$ Share of B = $\sf \dfrac{1}{3}$

Now, C is admitted with ¼ share in profits then,

Let, the share of profit be 1.

$\mapsto$ Share of C = $\sf \dfrac{1}{4}$

Then, the remaining share will be,

$\implies$ $\sf 1 - \dfrac{1}{4}$

$\implies$ $\sf \dfrac{4 - 1}{4}$

$\implies$ $\sf\bold{\dfrac{3}{4}}$

Again, we have to find the new share of A, B and C is,

$\leadsto$ New share of A :

$\implies$ $\sf \dfrac{2}{3} \times \dfrac{3}{4}$

$\implies$ $\sf\bold{\pink{\dfrac{6}{12}}}$

$\therefore$ The new share of A is $\sf\bold{\dfrac{6}{12}}$.

$\leadsto$ New share of B :

$\implies$ $\sf \dfrac{1}{3} \times \dfrac{3}{4}$

$\implies$ $\sf\bold{\pink{\dfrac{3}{12}}}$

$\therefore$ The new share of B is $\sf\bold{\dfrac{3}{12}}$.

$\leadsto$ New share of C :

$\implies$ $\sf \dfrac{1}{4}$

$\implies$ $\sf\bold{\dfrac{3}{12}}$

$\therefore$ The new share of C is $\sf\bold{\dfrac{3}{12}}$.

Now, we have to find the new ratio of A, B and C is,

$\implies$ $\sf \dfrac{6}{\cancel{12}} : \dfrac{3}{\cancel{12}} : \dfrac{3}{\cancel{12}}$

$\implies$ $\sf 6 : 3 : 3$

$\implies$ $\sf\boxed{\bold{\small{2 : 1 : 1}}}$

$\therefore$ The new ratio is 2 : 1 : 1 .

Answer 2

"23 : 13 : 12"

Explanation:

Old Ratio of A and B = 2 : 1

C's share = 1/4

A's sacrifice = 1/4 x 3/4 = 3/16

A's new share = 2/3 - 3/16 = 32-9/48 = 23/48

B's sacrifice = 1/4 x 1/4 = 1/16

B's new share = 1/3 - 1/16 = 16-3/48 = 13/48

C's share = 1/4 x 12/12 = 12/48

Therefore, new profit sharing ratio = 23 : 13 : 12