A and B can complete a piece of task together in 12 days while A alone can doit in 15
days. They start working together but A leaves 10 days before the completion ofthe task. For how many days did A and B work together?

Let the number of days taken by A to complete work as a.

Let the number of days taken by B to complete work as b.

So , according to question ,

$$\frac{1}{a} + \frac{1}{b} = \frac{1}{12}$$

=> $$\frac{1}{15} + \frac{1}{b} = \frac{1}{12}$$ =>$$ \frac{1}{b} = \frac{1}{60}$$

So , B takes 60 days to complete the task.

A/c the question , they worked together for some days and B worked alone for 10 days. Let x be the number of days they worked together.

$$(\frac{1}{15} + \frac{1}{60})x + \frac{1}{60} \times 10 = 1$$

$$\frac{1}{x} = \frac{1}{10}$$

So , the answer would be option b)10 days.