# Puzzle 32| (Completion of Task)

A man is allocated a task. He doubles the task done everyday. If the man completely does the task in 18 days, how many days did it take for the man to complete 25% of the task?

**Answer**: 16

100% of task = 18 days

As he doubles the task everyday. So,

50% of task = 17 days

25% of task = 16 days.

**Alternative Solution :**

Let the amount of work the man did on first day be **x** and total work to be done be **S**.

As the amount of work he did on next day would be 2 times of it’s previous day, we can write amount of work he did on 2^{nd }day as ‘2x’, 3^{rd} day ‘4x’, 4^{th} day ‘8x’ and so on….

We can write it as a GP as follows :

S = x+2x+4x+8x+….. (till 18^{th} day)

S = x*(2^{18}-1)/(2-1) [Formula of summation of GP S=a(r^{n}-1)/(r-1)]

S=x*(2^{18}-1) – *equation (1)*

According to ques we have to find the day when he would complete 25% of the total work, then ‘S’ becomes ‘S/4’

We can write the expression as

S/4 = x+2x+4x+8x+…. (till n^{th} day)

S/4=x*(2^{n}-1)/(2-1)

S/4=x*(2^{n}-1)

Substituting value of S from *equation (1)*

*x*(2 ^{18}-1)/4=x*(2^{n}-1)*

*On simplifying*

*2 ^{18}-1=4*(2^{n}-1)*

*2 ^{18}-1=2^{n}*4-4*

*2 ^{n+2}=2^{18}+3 (2^{n}*4=2^{n}*2^{2}=2^{n+2})*

We can neglect 3 in comparison of 2^{18}

2^{n+2}=2^{18}

n+2=18

n=16 days

So answer is 16 days.

This article is contributed by Vikash Kumar and Hardik Mittal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above