A can complete a task in 20 days while B can complete it in 30 days. In how many days can A and B working together complete it?

Correct option is D

Given:

A can complete the task in 20 days

B can complete the task in 30 days

Concept Used:

Combined work/day =$$\frac{1}{A's\ days} + \frac{1}{B's\ days}$$​

Time together =$$\frac{1}{\text{Combined work/day}}$$​

Solution:

Combined work/day =$$\frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60}$$

=$$\frac{5}{60} = \frac{1}{12}$$​

Time to complete the work together =$$\frac{1}{\frac{1}{12}} = 12 \text{ days}$$

Alternate Method:

Time to complete the work together = $$\frac {60}{3+2}=\frac{60}{5}= 12$$ days​