A and B can complete a work in 20 days and 30 days respectively. A works full time but B works half time. In how many days the entire work is to be completed?

A and B can complete a work in 20 days and 30 days respectively.

The LCM of 20 and 30 is 60 which can be assumed as the total work.

The efficiency of A = $$\frac{60}{20}$$ = 3 units/day

The efficiency of B = $$\frac{60}{30}$$ = 2 units/day

A works full time but B works half time.

So work done by A in one day = 3 units

B is working half-time. So the work done by B in one day = $$\frac{1}{2}\times\ 2$$ = 1 unit

Work done by A(full time) and B(half-time) together in one day = 3+1 = 4 units

Number of days taken by both of them to complete the entire work = $$\frac{60}{4}$$

= 15 days