Question

A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. How many men were originally there?

Answer 1

Hint: Work done with an original and new number of men will be the same (responsible for performing the same work). So we can calculate the work done in both the cases (with original and with added men) and equate them.
Formula for work done to be used here:
Work done = Men involved X Time taken

Complete step-by-step answer:
The total work done will be given by the product of number of men and the time taken to complete the work:
Work done = Number of men X Number of days
Let the number of men involved originally be x
The work done in first case will be:
 $\Rightarrow W.{D_1} = x \times 60 $ as the work was completed in 60 days
In the second case, 8 more men were added, the number of men increases by 8 and become:
x + 8
The work finished in 10 days less🡪 60 – 10 = 50
So, the work done in second case will be:
 $\Rightarrow W.{D_2} = \left( {x + 8} \right) \times 50 $
The total work is same for both the cases, which means:
 $\Rightarrow W.{D_1} = W.{D_2} $ , this gives:
 $ x \times 60 = (x + 8) \times 50 $
$\Rightarrow$ 6x = 5(x + 8)
$\Rightarrow$ 6x = 5x + 40
$\Rightarrow$ 6x – 5x = 40
$\Rightarrow$ x = 60
Therefore, for the given work, there were 60 men originally before 8 more were added.

Note: The proportionalities among the work, person and time are to be noted:
Work done is directly proportional to persons = more work requires more persons.
Time is inversely proportional to persons = more people will complete the work in less amount of time. Work and time are directly proportional = more work requires more time to be completed.