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Puzzle 32| (Completion of Task)

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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 w   

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 done by 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 result in 2 times of work done on it’s previous day, we can write amount of work he done at the end of  2nd day as ‘2x’, 3rd day ‘4x’, 4th day ‘8x’ and so on….

Therefore , at end of 18th day, work done will be 217 x.

S = 217x.  –   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*2n-1(at the end of nth day)

Substituting value of S from equation (1)

x*(217)/4=x*(2n-1)

On simplifying

217=4*(2n-1)

217=2n+1

n+1=17

n=16 days

So answer is 16 days.


 


Last Updated : 19 Jan, 2023
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