Question

divide 34 in two parts in such a way that 4/3 of one part is equal to 2/5 of other

Answer 1

let x and y be the two parts.
by given condition
x+y=34
----------(1)
4x/3=2y/5
20x=6y
20x-6y=0
10x-3y =0 (dividing both sides by 2)
-----------(2)
multiplying eq. (1) by3
3x+3y=102
-------(3)
adding eq. (2) and eq (3)
10x-3y=0
+ 3x+3y =102
----------------------------
13x = 102
x=102/13
x=7 .0853
substitute x=7.08553 in eq (1)
x+y=34
7.0853+y =34
y=34-7.0853
=26.9147
the two parts are
7.0853 and 26.9147