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?

An experienced carpenter can complete a woodwork in 8 days. A young carpenter can complete the same work in 12 days.

So the LCM of 8 and 12 is 24 which can be assumed as per the total work.

The efficiency of an experienced carpenter = $$\frac{24}{8}$$ = 3 units/day

The efficiency of a young carpenter = $$\frac{24}{12}$$ = 2 units/day

Both work together for 3 days, and then the latter leaves.

Let's assume the time taken by the former(experienced carpenter) to complete the remaining work is 'y'.

$$3\times(3+2) + y \times3 = 24$$

$$3\times5 + y \times3 = 24$$

5+y = 8

Time taken by the former to complete the remaining work = y = 8-5 = 3 days