You require a simultaneous equation method I assume.

At first,

Khairul : Michael : Ethan
6 : 4 : 5

Let Khairul, Michael and Ethan's money be $6x, $4x and $5x respectively.

After he gives Michael $30 and Ethan $15,

Khairul : Michael : Ethan
7 : 6 : 7

Let Khairul, Michael and Ethan's money now be $7y, $6y and $7y respectively.


From here we can form the following equations:

Based on the change in Michael's amount of money,
4x + 30 = 6y
Simplifying,
2x + 15 = 3y ①

Based on Ethan's change,
5x + 15 = 7y ②

Using the method of elimination, make the coefficient of y the same to eliminate the terms in y.

7 × ① 3 × ② :

7(2x + 15) - 3(5x + 15) = 7 × 3y - 3 × 7y

14x + 105 - 15x - 45 = 0
60 - x = 0
x = 60

Amount of money Khairul had initially = $6x
= $(6 × 60)
= $360

Alternatively, realise that Khairul and Ethan had the same amount of money after Khairul gave away the $30 and $15, and Ethan received $15.

(They ended up with the same ratio of 7)


Khairul's initial - amount given to the other two = Ethan's initial + amount received

6x - 30 - 15 = 5x + 15
6x - 5x = 30 + 15 + 15
x = 60

Khairul's initial amount
$6x = $(6×60) = $360