Question

If 12 men working 8 hours a day can complete a task in 16 days. If the same task must be completed in 8 days, how many more people would be required if all of them work for 12 hours?

Answer 1

Hint: The total amount of work to be done remains constant irrespective of the factor of who is doing the work. Let the work capacities of the male workers be x per hour. So, the total work to be finished comes to be $8\times 16\times 12x$ , in terms of x.

Complete step-by-step answer:
To start with the solution, we let the work done by a male worker per hour be x.
$nk\times \sum{\left( \text{work capacity of each worker working} \right)\text{.}}$
Now, try to interpret the statement given in the question in mathematical terms using the above formula, we get:
$\text{Total work that needs to be completed=8}\times \text{16}\times \text{12x}.........\text{(i)}$ .
Total work is independent of the number of workers and the type of worker doing the work.
Now we let the number of additional male workers required to be p, to finish the work in 8 days.
$\text{Total work that needs to be completed = }nk\times \sum{\left( \text{work capacity of each worker working} \right)\text{.}}$
$\Rightarrow \text{Total work that needs to be completed = 8}\times \text{12}\times \left( p+12 \right)x$ .
Substituting Total work from equation (i).
$8\times \text{16}\times \text{12}x\text{ = 8}\times \text{12}\times \left( p+12 \right)x$
$\Rightarrow 16\text{ =p+12}$
$\therefore p=4\text{ male workers}$
Therefore, we can say that the answer to the above question is 4 men.

Note: Questions, including work, have two things to be wisely selected. One is the elements of the problem that we are treating as variables, and the other is the unit of work. We can either let work done per unit time of each worker as variables or the total work to be a variable. The choice of unit and element for variable decides the complexity of solving.