3 children eat 4 kilos in 5 days means that 1 child eats 4/3 kilos in 5 days, that is, 1 child eats (4/3)/5 = 4/15 kilos per day.

12 children will eat 12*(4/15) = 16/5 kilos per day.

We divide the total amount of rice 48 by 16/5 and get:

48 : (16/5) = 48*5/16 = 15 days

12 children eat 48 kilos of rice in 15 days.

Another way to solve this problem is:

3 kids eat 4 kilos in 5 days

Since the number of kids is directly proportional to the number of kilos we have:

3*4 = 12 kids eat 4*4 =16 kilos in 5 days

Also the amount of rice eaten is directly proportional to the number of days we have:

12 kids will eat 16*3 = 48 kilos in 5*3 = 15 days.