First two look ok. The last one is not exactly correct, because they take a total of 12 “man-hours” to complete everything regardless of the number of men working on it (which is technically the 12 hours you mentioned in the second method).

Usually I would just skip the 12 man-hours and just do multiplication and division.

how would u explain why the last method is incorrect ? technically it also involves division and multiplication haha

The idea is that the total time remains unchanged, and not a proportion.

So here it would be 12 man-hours as the total time and not 12 hours.

btw how to justify why total hrs must remain unchanged ?

Because the amount of work done remains unchanged in the first place. It’s like an identical building is to be built again except that a different number of people acts on the same job.

So, if a building is to be completed by two people, they share the workload so that each person does half the building, but as a whole, the same proportion of building is completed.

The “man-hours” which I have referred to here is basically the amount of building to be completed (100% of the entire building), not really hours.

So a homework which is two pages long can be thought of as to be completed in a single person by 2 hours. We call this “man-hours”, the overall total time spent by each of the students as a whole, but this remains unchanged.

Two person who share the same homework, and thus complete one page each, contributes to a total of 2 man-hours of work (1 man-hour from each person because each person only completes one page of homework).

The total hours only remains unchanged if the efficiency and productivity of each person remains the same and equal to each other.

Alternative method

Assuming the men have the same productivity and efficiency/work-rate ,

If 2 men take 6 hours each to build the car,

Then each man builds ½ the car in 6 hours.



In 1 hour,
½ x 1/6 = 1/12

Each man builds 1/12 of the car in 1 hour.


For 3 men,
1/12 x 3 = 3/12 = 1/4

3 men build 1/4 of the car in 1 hour.

So they will need 4 hours each to build the whole car.

If you use method 3,

Then 1 man would need 24 hours to complete the whole car if he worked alone.

But that is not correct as 1 man can complete ½ the car in 6 hours. So he'll only need 12 hours in total to build the whole car


Method 3 cannot work as you could then also write 1 man : 12 hours total

So we can't multiply and divide in a similar fashion to method 2.

You can take 1 man-hour as the amount time spent working by 1 person in an hour


So if 50000 people work together, for 1 hour in the same time, 50000 man-hours have elapsed. But in reality only 1 hour has passed.

thanks all for the detailed explanation :)