Question

Ajit can complete a piece of work in 60 days, whereas kailash and shailendra working together can complete it in 15 days. When ajit and shailendra alternately work for a day each, the work gets completed in 40 days. The number of days in which kailash will complete twice the work is

Answer 1

In 60 days Kailash will complete twice the work alone.

Step-by-step explanation:

Let assume that Shailendra can complete the work alone in x days.

Now, Ajit can complete the same piece of work in 60 days.

So, when Ajit and Shailendra alternately work for a day each, then in two days they will do $(\frac{1}{60} + \frac{1}{x})$ part of the work.

So, from the given condition, we can write the equation

$20(\frac{1}{60} + \frac{1}{x}) = 1$

⇒ $(\frac{1}{60} + \frac{1}{x}) = \frac{1}{20}$

⇒ $\frac{1}{x} = \frac{1}{20} - \frac{1}{60} = \frac{1}{30}$

⇒ x = 30 days.

Now, assume that Kailash can complete the work in y days alone.

So, we can write the equation

$\frac{1}{y} + \frac{1}{30} = \frac{1}{15}$

⇒ $\frac{1}{y} = \frac{1}{30}$

⇒ y = 30 days.

Therefore, in 30 days Kailash will complete the work alone.

Hence, in 60 days Kailash will complete twice the work alone. (Answer)