40 boys eat 40 cakes in 40 days

So, 1 boy will eat 1 cake in 40 days

And, 1 boy will eat (1/40) of a cake in one day

So, 15 boys will eat 15*(1/40) cake in a day

Hence, days required for 15 boys to eat 18 cakes = (18)/(15/40) = (18*40)/15 = 48

15 boys will eat 18 cakes in 48 days