Question

Assume x and y have 5:3 profit sharing ratio respectivly and a new member enters by taking 1/5 from x and 1/3 from y.what will be the new ratio of the three people?

Answer 1

The original proportion: x : y = 5:3 ---> x/y = 5/3 ---> x = 5y/3
after change:
first member : (4/5)x or 4x/5
2nd member: (2/3)y or 2y/3
new member: (1/5)x + (1/3)y or x/5 + y/3
new ratio : 4x/5 : 2y/3 : (x/5 + y/3)
= 4(5y/3)/5 : 2y/3 : (5y/3)/5 + y/3)
= 4y/3 : 2y/3 : 2y/3
= 4 : 2 : 2
= 2 : 1 : 1

check: suppose the original investments were $600 and $360
(notice 600:360 = 5:3)
first member left with 480
2nd member left with 240
new member has 120+120 = 240
ratio = 480 : 240 : 240 = 2:1:1
my answer is plausible

Answer 2

how do we get the 4x/5 and 2y/3

Answer 3

First member started with x
you took 1/5 away, leaving him with 4/5
(4/5)x = 4x/5

same steps for 2y/3