P and Q can do work separately in 10 and 20 days, respectively. In how many days can they finish it, working together?

20/3

The correct answer is Option (2) → 20/3

We are asked: P can do a work in 10 days, Q in 20 days. Find the time they take together.

Step 1: Work rates

• P’s 1 day work = $\frac{1}{10}$​
• Q’s 1 day work = $\frac{1}{20}$

Step 2: Combined 1 day work

$\frac{1}{10} + \frac{1}{20} = \frac{2}{20} + \frac{1}{20} = \frac{3}{20}$

Step 3: Time to complete work together

$\text{Time} = \frac{1}{\text{Combined work/day}} = \frac{1}{3/20} = \frac{20}{3} \text{ days}$