Answer:
:
Let Vijay's age be x years
Shyam's age = 6 years (given)
Ajay's age = Shyam's age + Vijay's age = (x + 6) years
$\therefore$ Ajay's share = $\frac{x+6}{x+6+(x+6)}\times amount=\frac{1}{2}\times 1080$= Rs 540
When Ajay takes Rs 540, the balance amount left would be Rs 540
$\therefore$Vijay's share = $\frac{x}{2(x+6)}\times 540.$ His actual share = $\frac{x}{2(x+6)}\times 1080$
The difference between these two amounts is Rs 180 (which he received in the evening from his father)
$\therefore$ $\frac{x}{2(x+6)}\times 1080-\frac{x}{2(x+6)}\times 540=180$
x = 12 years
$\therefore$ Vijay's actual share = $\frac{12}{2\times 18}\times 1080$= Rs. 360
Out of this,
He received Rs 180 later. Hence, he should have taken Rs 180 initially. Balance amount left when shyam came home was = 1080 - (540 + 180)
= Rs. 360
Out of this, the amount Shyam took
$=\frac{6}{2(x+6)}\times 360$
$=\frac{6}{2\times 18}\times 360$= Rs 60