Completion of Task | Puzzles for Interview - Interview Preparation PDF Download

Introduction

A man was given a task to complete. He doubled the amount of work done every day. The task was completed in 18 days. The puzzle is to find out how many days it took him to complete 25% of the task.

Solution 1: Using Percentage

To solve this puzzle, we need to use the concept of percentages. If the man doubled the task done every day, then we can divide the task into halves. So, if the complete task was done in 18 days, then half of the task was done in 17 days. Similarly, 25% of the task would be done in 16 days. Therefore, the man took 16 days to complete 25% of the task.

Solution 2: Using Algebra

Another way to solve this puzzle is by using algebraic equations. Let us assume that the amount of work done by the man on the first day was 'x', and the total work to be done was 'S'. As the man doubled the amount of work every day, we can write the amount of work done on the second day as '2x', on the third day as '4x', and so on. Therefore, the work done at the end of the 18th day would be 217x.
We can now write an equation as S = 217x. This equation shows that the total work to be done is 217 times the work done on the first day. Now, we need to find out how many days it took for the man to complete 25% of the task. If we assume that the number of days taken to complete 25% of the task was 'n', then the amount of work done at the end of the nth day would be 2n-1 times the amount of work done on the first day. So, we can write an equation as S/4 = x*2n-1.
We can now substitute the value of S from the previous equation and simplify the expression. After simplification, we get the equation 217 = 4*(2n-1). On solving this equation, we get n = 16. Therefore, it took the man 16 days to complete 25% of the task.

Conclusion

In summary, the man took 16 days to complete 25% of the task. We can solve this puzzle using either percentages or algebraic equations.