A man, a woman and a boy can do a work individually in 3, 4 and 12 days respectively. How many boys are to be employed to help 3 men and 4 women to finish the work in $$\frac{1}{4}$$ of a day?

Man = 3 days

Woman = 4 days

boy = 12 days

Total work done = LCM (3,4,12)= 12

Man's efficiency = $$\frac{12}{3}$$ = 4

Woman's efficiency = $$\frac{12}{4}$$ = 3

boy 's efficiency = $$\frac{12}{12}$$ = 1

Total days= $$\frac{12}{8}$$days

N no. Of  boys are to be employed to help 3 men and 4 women to finish the work in $$\frac{1}{4}$$ of a day

so

as we know that ,

efficiency multiplied by time = work

3 men = $$3\times 4$$ =12

4 women = $$4\times 3$$ = 12

$$12\times \frac{1}{4} + 12\times \frac{1}{4}+ N\times \frac{1}{4}$$= 12

N = 24 boys