Question

A, B and C share profit in the ratio 1/4:1/6:7/12. If C retire, what are the new profit ratio of A and B, while they share the profit of C in the ratio 4:5 respectively. ​

Answer 1

Answer:

A: B :: 55 : 53

Step-by-step explanation:

A : B : C :: 1/4 : 1/6 : 7/12

A + B + C = 1/4 + 1/6 + 7/12 =  (1/12) (3 + 2 + 7) = 12/12 = 1

A share = 1/4

B Share = 1/6

C share = 7/12

A share out of C share = (4/(4+5)) * (7/12) = (4/9)  * (7/12) = 28/108

B Share out of C share = (5/(4+5)) * (7/12) = (5/9)  * (7/12) = 35/108

A Share with 4/9 of C Share  =  1/4 + 28/108  = 55/108

B Share with 5/9 of C share = 1/6 + 35/108 = 53/108

A: B share ::  55/108 : 53/108

A: B :: 55 : 53

Answer 2

Answer:

New Profit Ratio is 55 : 53

Step-by-step explanation:

Given Profit Share of A , B & C are $\frac{1}{4}:\frac{1}{6}:\frac{7}{12}$

         Share of C is shared between A & B in ration 4 : 5

To find: New Profit Ratio of A & B

Profit Share of A , B & C = $\frac{1}{4}:\frac{1}{6}:\frac{7}{12}$

                                        = $\frac{3}{12}:\frac{2}{12}:\frac{7}{12}$

                                       = 3 : 2 : 7

let the profit share of A = 3x , the profit share of B = 2x and the profit share of C = 7x

Now we divide C's Share 7x in A & B in ration 4:5

Share that A recieve = $\frac{4}{4+5}\times7x=\frac{4}{9}\times7x=\frac{28x}{9}$

Share that B recieve = $\frac{5}{4+5}\times7x=\frac{5}{9}\times7x=\frac{35x}{9}$

New Share profit of A = $3x+\frac{28x}{9}=\frac{27x+28x}{9}=\frac{55x}{9}$

New Share profit of B = $2x+\frac{35x}{9}=\frac{18x+35x}{9}=\frac{53x}{9}$

New Profit ratio = $\frac{55x}{9}\::\:\frac{53x}{9}$

                          = 55 : 53

Therefore, New Profit Ratio is 55 : 53