Puzzle | Completion of Task

A man is assigned a task and doubles the amount of work he does each day. If he completes the entire task in 18 days, how many days does it take him to complete 25% of the task?

Check if you were right - full answer with solution below.

Solution:

Let the man do x units of work on Day 1. Since the work doubles each day, the amount of work done on Day 2 is 2x, Day 3 is 4x and so on.

 So, the total work done by the end of Day 18 is:

This is a geometric series with a first term and a common ratio . The sum of the first 18 terms is:

We are asked to find the day when the man completes of the total work, i.e.

Let the cumulative work done by the end of daybe:

Now, equating this to

Cancel from both sides:

Solving for :

Since,

Therefore, the man completes 25% of the task by the end of Day 16.

Simple Method:

When 100% of the work is completed in 18 days, and the work doubles every day.

50% of the work would be completed on day 17.

Therefore, 25% of the work would have been completed in 16 days.