Question

A and B together can complete a work in 20 days while A is 25% more efficient than B, then find in how many days the work will be complete if they work on alternate days starting with A?

Answer 1

Answer:

63 days

Step-by-step explanation:

Answer 2

They will complete the work in 30 days.

Step-by-step explanation:

Let us assume that A can complete in x days.

As A is 25% more efficient than B, then B will complete the job in $x(1 + \frac{25}{100}) = 1.25x$ days.

Now, together they will do in one day $(\frac{1}{x} + \frac{1}{1.25x}) = \frac{1 + 1.25}{1.25x} = \frac{2.25}{1.25x} = \frac{1.8}{x}$ part of the job.

So, they will complete the job together in $\frac{x}{1.8}$ days.

Hence, given that  $\frac{x}{1.8} = 15$

⇒ x = 27 days.

Therefore, A can do the job in 27 days alone and B will do the job in (27 × 1.25) =33.75 days alone.

Now, if they work on alternate days starting with A, then after 2 days they will complete $(\frac{1}{27} + \frac{1}{33.75}) = \frac{1}{15}$ part of the job.

So, they will complete the work in $2 \div \frac{1}{15} = 30$ days. (Answer)