A can do a work in 20 days and B in 30 days. If they work on it together for 2 days, then what is the fraction of the work that is left?

The correct option is 5/6.

Step-by-step explanation:

Step 1: Determine the rate of work for A and B per day.
A can complete the full work in 20 days. Therefore, work done by A in 1 day = $\frac{1}{20}$
B can complete the full work in 30 days. Therefore, work done by B in 1 day = $\frac{1}{30}$

Step 2: Find the combined work done by both in 1 day.
Work done by (A + B) in 1 day = $\frac{1}{20}+\frac{1}{30}$
Taking the least common multiple (LCM) of 20 and 30, which is 60:
Work done by (A + B) in 1 day = $\frac{3+2}{60}=\frac{5}{60}=\frac{1}{12}$

Step 3: Calculate the work completed in 2 days.
Work done in 2 days = $2\times \frac{1}{12}=\frac{2}{12}=\frac{1}{6}$

Step 4: Calculate the remaining fraction of work.
Fraction of work left = $1-\frac{1}{6}=\frac{6-1}{6}=\frac{5}{6}$

Thus, the fraction of work that is left is 5/6.