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?

360 days

N + K = 240 days, K + G = 72 days, N + G = 80 days,

⇒ Adding all the efficiencies,

⇒ 2(N + K + G) = 22

⇒ N + K+ G = 11,

Now,

⇒ N + 10 = 11,

⇒ N = 1,

⇒ N + K = 3,

⇒ 1 + K = 3,

⇒ K = 2,

Therefore time required by K to complete total work = \(\frac{720}{2}\) = 360 days,    ..(\(\frac{Work}{Efficiency}\) = Time)