X and Y can do a piece of work in 20 days and 12 days

• Time Work

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

1. 6 days
2. 10 days
3. 20 days
4. 15 days

Solution

Let total work that has to be done is 120 units (common multiple of 20 and 12). 

In one day, X can do 6 units and Y can do 10 units of work. Thus, they both can do 16 units of work in a day.

In 4 days, X did (6 * 4) or 24 units of work.

After 4 days, work left to be done = 120 - 24 = 96.

Now, both X and Y work till the completion of work. They can do 16 units of work in one day. To complete at 16 units per day, 6 more days will be more required.

Total days = 4 + 6 = 10

The correct option is B.