A can do a work in 4 days and B in 12 days. If they work on it together for 2 days, then the fraction of the work that will be left is:

Correct option is C

Given:

A can complete the work in 4 days, and B can complete it in 12 days. We need to find the fraction of the work left after they work together for 2 days.

Solution:

Work done by A in 1=  day $$\frac{1}{4}$$​​

Work done by B in 1 day = $$\frac{1}{12}$$​​

Work done by A and B together in 1 day =$$\frac{1}{4} + \frac{1}{12}$$​​

Work done by A and B together in 1 day = $$\frac{(3+1)}{12} = \frac{1}{3}$$​​

Work done by A and B together in 2 days = $$2\times \frac{1}{3} = \frac{2}{3}$$​​

Fraction of work left = $$1 - \frac{2}{3} = \frac{1}{3}$$​​

Therefore, the fraction of the work that will be left is $$\frac{1}{3}.$$​​