Amother has 3 kids. kid a is half the mother's current age. kid b is 4 years younger than kid a. in 3 years, kid c will be 1/5 of his mother's age (not her current age). the sum of all their current ages is the mother's current age.

how old is the mother currently?

how old is each of her kids?

Let the age of the mother be G.

i)
"Kid A is half the mother's current age."

thus, the age of Kid A is G/2

ii)
"Kid B is 4 years younger than Kid A."

this means, the age of Kid B is the age of Kid A - 4 = G/2 - 4

iii)
"In 3 years, Kid C will be 1/5 of his mother's age (not her current age). "

thus, in 3 years the age of Kid C will be 1/5(G+3)=1/5G+3/5

this means that the current age of Kid C is

1/5G+3/5-3=1/5G+3/5-15/5=1/5G-12/5 = (G-12)/5

The ages of the Kids A, B and C are: 

G/2 , G/2 - 4, (G-12)/5

From the smallest Child's age (G-12)/5 we understand that G-12 is a multiple of 5, 

so G-12 ∈{5, 10, 15, 20, 25, }

which means G∈{17, 22, 27, 32, 37, 42, 47, 51, 56, 61... }

From the age of the oldest child G/2, we understand that G must be an even number (so that G/2 is a whole number).

This means that G∈{22, 32, 42, 56,...}

If G was 22, the oldest child would be 11, which makes no sense

If G is 32, the oldest child is 16, which means the woman became a mother at the age of 16, which is rare, but possible.

then G/2=16 , G/2 - 4=12, (G-12)/5=(32-12)/5=20/5=4

If G is 42, her oldest child is 21, no more a "kid", but still, lets consider this case:

the age of the second child is 21-4=17, and the youngest (42-12)/5=6

The Plausible cases are :

i) mother: 32, children 16, 12, 4
ii) mother: 42, children : 21, 17, 6