P can complete five-eighths of a work in 15 days and Q can complete three-fourths of the same work in 30 days. They worked together for 8 days and then P left. How much time will Q working alone, take to complete the remaining work?

18 days 16 hours

P = \(\frac{5}{8}\)W = 15 days = 24 days,

Q = \(\frac{3}{4}\)W = 30 days = 40 days,

⇒ P + Q worked for 8 days and then P left = (5 + 3) x 8 = 8 x 8 = 64 days,   ..(Efficiency × Days = Total work)

⇒ Remaining work = 120 - 64 = 56 units,

⇒ Time required by Q to complete remaining work = \(\frac{56}{3}\) = \( { 18}_{3 }^{2 } \) x 24 = 18 days 16 hours.        ..(\(\frac{Work}{Efficiency}\) = Time)