Question

A man working $8$hours a day takes $5$days to complete a project. How many hours a day must he work to complete it in $4$days?
A) $10$ hours
B) $11$ hours
C) $12$ hours
D) $14$ hours

Answer 1

Hint: If a man wants to finish the target earlier, he would have to increase his daily productivity or we can say that daily working time. In this type of questions evaluate the total work and then evaluate the rest of the things according to the question.

Complete step-by-step answer:
We are given that a man working $8$hours a day takes $5$days to complete a project.
We have to find how many hours a day must he work to complete it in $4$days?
He wants to complete his project earlier; it means he has to increase the number of hours on a daily basis so that he could complete the project in $4$days.
First, we evaluate the total work that is the product of time and days.
Total work will be $8 \times 5 = 40$
We assume that he is completing $40$questions of a project in $5$ days working $8$hours a day.
Now, he wants to finish it off in $4$ days.
In order to evaluate the daily hours, we divide the total number of questions by the total number of days.
That is,
$\dfrac{{40}}{4} = 10$
Therefore, if he wants to finish his project in $4$ days, he has to work $10$hours on a daily basis.
Hence, option (A) is correct.
Note: We can solve it by another method which is shown below:
We use the formula ${M_1}{D_1}{H_1} = {M_2}{D_2}{H_2}$
Here$M$represents man, $D$ represents days and $H$represents hours
Since there is only one man so we can exclude the $M$ factor.
Substitute all other values and evaluate ${H_2}$
$
  8 \times 5 = 4 \times {H_2} \\
  {H_2} = 10 \\
 $
Hence, option (A) is correct.