Question

Divide 120 into 2 parts such that 2/3 of one part is equals to 2/5 of other part

Answer 1

Let one part be 2x/3 and other be 2y/5.
Given,
2x/3 = 2y/5
And 2x/3 + 2y/5 = 120
So we can also write,
2x/3 + 2x/3 = 120 [ 2y/5 = 2x/3]
or 4x/3 = 120
or x = 120*3/4
or x = 90

So,
First part = 2*90/3 = 60
Second part = 120 - 60 = 60

Answer 2

Let the parts be x and y

x + y = 120 --------(1)

2x/3 = 2y/5

5(2x) = 3(2y)

10x = 6y

10x - 6y = 0 --------(2)

Multiply 6 on both sides for equation (1):-

6x + 6y = 72 -------(3)

(3)+(2)

6x + 6y = 720
10x - 6y = 0
--------------–-
16x = 720

x = 720/16

x = 45

x + y = 120

45 + y = 120

y = 120-45

y = 75

Therefore, 120 is divided into 2 parts.

2 parts are 45 and 75

Hope it helps