N and K together can complete a work in 240 days. K and G together can complete the same work in 72 days and N and G together can complete the same work in 80 days. In how many days K alone can complete the same work?

The LCM of 240, 72 and 80 is 720 which can be assumed as the total work.

N and K together can complete a work in 240 days.

Efficiency of N and K together = $$\frac{720}{240}$$ = 3 units/day

K and G together can complete the same work in 72 days.

Efficiency of K and G together = $$\frac{720}{72}$$ = 10 units/day
N and G together can complete the same work in 80 days.

Efficiency of N and G together = $$\frac{720}{80}$$ = 9 units/day

Efficiency of N, K and G together = $$\frac{\left(3+10+9\right)}{2}$$
= $$\frac{22}{2}$$

= 11 units/day

Efficiency of K = Efficiency of N, K and G together - Efficiency of N and G together

= 11-9

= 2 units/day

Number of days taken by K alone to complete the same work = $$\frac{720}{2}$$

= 360 days