A can do a piece of work alone in 40 days. A and B together can do the same work in 10 days. C is 50% less efficient than B. In how many days can A and C together complete the same work?

Let's assume the total work is 40 units.

A can do a piece of work alone in 40 days.

Efficiency of A = $$\frac{40}{40}$$ = 1 unit/day    Eq.(i)

A and B together can do the same work in 10 days.

Efficiency of A and B together = $$\frac{40}{10}$$ = 4 units/day    Eq.(ii)

Efficiency of B = Eq.(ii)-Eq.(i)

= 4-1

= 3 units/day

C is 50% less efficient than B.

Efficiency of C = 3 of (100-50)%

= 3 of 50%

= $$3\times\frac{50}{100}$$

= $$3\times\frac{1}{2}$$

= 1.5 units/day

Time taken by A and C together to complete the same work = $$\frac{40}{1+1.5}$$

= $$\frac{40}{2.5}$$

= $$\frac{400}{25}$$

= 16 days