P can complete a piece of work in 18 days, while Q can complete the same work in 36 days. If both P and Q work together, in how many days will they be able to complete the entire work?

Question: P can complete a piece of work in 18 days, while Q can complete the same work in 36 days. If both P and Q work together, in how many days will they be able to complete the entire work?

Solution:
Given that,
P can do a piece of the work in 18 days and Q can do same work in 36 days

Now,
Let the total work = LCM(18, 36) = 36

Hence, total work = 36 units

Thus,
P does each day = 36 ÷ 18 = 2 units
Q does each day = 36 ÷ 36 = 1 unit

Hence, time taken by them to finish the work together = 36 ÷ (1 + 2) = 12 days.

∴ In 12 days working together they will complete the entire work.