P and Q can complete a work in 9 days and 15 days, respectively. If they work together for three days, then in how many days will the remaining work be completed by Q alone?

7

P = 9 days, Q = 15 days,

⇒ P + Q worked for 3 days = (5 + 3) x 3 = 8 x 3 = 24 units,   ..(Efficiency × Days = Total work)

⇒ Remaining work = 45 - 24 = 21 units,

⇒ Time required by Q to complete remaining work = \(\frac{21}{3}\) = 7 days, ..(\(\frac{Work}{Efficiency}\) = Time)