'A' and 'B' together can do some work in 24 days.

Solution

Let the total work be 48 units. {LCM (24 and 16)}

So, combined efficiency of 'A' and 'B' = 48 ÷ 24 = 2 units/day

And combined efficiency of 'A' and 'C' = 48 ÷ 16 = 3 units/day

Let the efficiency of 'A' and 'C' be 'x' units/day and 'y' units/day, respectively.

So, efficiency of 'B' = y X 0.5 = '0.5y' units/day

So, x + y = 3 ....... (I)

And, x + 0.5y = 2 ...... (II)

On subtracting equation (II) from equation (I), we have;

0.5y = 1

So, y = 2

So, efficiency of 'B' = 2 X 0.5 = 1 units/day

So, required time = 48 ÷ 1 = 48 days