An experienced carpenter can complete a woodwork in 8 days. A young carpenter can complete the same work in 12 days. Both work together for 3 days, and then the latter leaves. How many days will be taken by the former to complete the remaining work?

3

Experienced Carpenter (EC) = 8 days,

Young Carpenter (YC) = 12 days,

⇒ Both of the worked together for 3 days = (3 + 2) x 3 = 5 x 3 = 15 units,  ..(Efficiency × Days = Total work)

⇒ Remaining work = 24 - 15 = 9 units,

⇒ Time required by EC to complete remaining work = \(\frac{9}{3}\) = 3 days,   ..(\(\frac{Work}{Efficiency}\) = Time)