P and Q can complete a job in 12 days and 16 days respectively. They work together for 4 days. What portion of work is left for completion?

Correct option is C

Given: 

P can complete the work = 12 days 

Q can complete the work = 16 days 

​Solution:​

Let the total work be represented as 1 unit.

P can complete the work in 12 days, so P's rate of work is: $$\frac{1}{12}$$​  of the work per day.

Q can complete the work in 16 days, so Q's rate of work is:  $$\frac{1}{16}$$​ of the work per day.

Together, P and Q's rate of work is:   $$\frac{1}{12} + \frac{1}{16} = \frac{4 + 3}{48} = \frac{7}{48}$$​ of the work per day.

In 4 days, P and Q together can complete:   $$4 \times \frac{7}{48} = \frac{28}{48} = \frac{7}{12}$$​ of the work.

Thus, the portion of work left is: $$1 - \frac{7}{12} = \frac{5}{12}$$​.

Hence, $$\frac{5}{12}$$​ of the work is left for completion.