A and B can complete a certain task in 24 days  and 40 days, respectively. They worked together for 8 days. C completed the remaining task in 14 days. Working together, A and C will complete 75% of the same work in :

10 days 

A = 24 days, B = 40 days,

⇒ A + B worked for 8 days = (5 + 3) x 8 = 8 x 8 = 64 units,

⇒ Remaining work = 120 - 64 = 56 units,

⇒ Remaining work is completed by C in 14 days = \(\frac{56}{C}\) = 14 days,

⇒ C = \(\frac{56}{14}\) = 4,  (Efficiency)

⇒ \(\frac{3}{4}\) of total work = \(\frac{3}{4}\) x 120 = 90 units,

⇒ Time required for A + C to complete 90 units of work = \(\frac{90}{5+4}\) = \(\frac{90}{9}\) = 10 days.   ..(\(\frac{Work}{Efficiency}\) = Time)