Question

The ratio of the number of marbles Ali has to Bob and Charlie is 1:2:3. Ali decided to
give Bob 1/3 of his share. Bob then decided to give Charlie 2/5 of his share. Charlie then decided
to give Ali 1/4 of his share. Find the ratio of the number of marbles Ali has to Bob to Charlie in
the end.

Answer 1

Right now:
Ali has x
Bob has 2x
Charlie has 3x

first action:
Ali gives Bob 1/3
so Ali now has (2/3)x
Bob has 2x + (1/3)x = 7x/3
Charlie still has 3x

2nd action: Bob gives Charlie 2/5 of (7/3)x or (14/15)x
Bob now has 7x/3 - 14x/15 = 7x/5
Charlie now has 3x + 14x/15 = 59x/15
Ali still has 2x/3

3rd action: Charlie gives Ali 1/4 of his share
Charlie now has 59x/15 - (1/4)(59x/15) = (3/4)(59x/15) = 59x/20
Ali now has 2x/3 + (1/4)(59x/15) = 33x/20
Bob still has 7x/5

Ali : Bob : Charlie = 33x/20 : 7x/5 : 59x/20
= 33x : 28x : 59x
= 33 : 28 : 59

check my arithmetic