Question

A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally ?
A. 72
B. 82
C. 100
D. 110

Answer 1

Hint: We have to find the number of men originally present at the beginning. Let us assume this value to be \[x\] . Hence, the total work effort $=100x...(i)$ . 10 men were on leave, that is, $x-10$ that leads to the completion of the work in 10 more days, that is, 110 days. Hence, we get total work effort for this criteria as $110(x-10)...(ii)$ . When we equate equations (i) and (ii) since the same work piece is completed, we will get an expression and by solving this, we get the value of $x$ .

Complete step by step answer:
It is given that 100 days are required to complete a piece of work by a certain number of men. Also if 10 men were on leave, the work will be completed in 10 more days, that is , 110 days. We have to find the number of men originally present from the beginning.
Let us assume \[x\] to be the number of men originally present at the beginning.
Hence, the total work effort $=100x...(i)$
Now, when 10 men is on leave, the remaining men $=x-10$
Thus, total work effort will be $=110(x-10)...(ii)$
The final work is the same. Hence, we can equate equations (i) and (ii). Thus we get
$100x=110(x-10)$
Now, let us expand the RHS. We will get
$100x=110x-1100$
The above equation can be modified by collecting the constants on one side and variables on another. Then, we will get
$110x-100x=1100$
Let us now apply the subtraction operation on the above equation. We get
$10x=1100$
This can be written as
$x=\dfrac{1100}{10}$
Hence, we get
$x=110$
Thus, the total number of men originally present at the beginning is 110.

So, the correct answer is “Option D”.

Note: Be careful when framing equations. You may make errors when making the equation $x-10$ when 10 men are on leave. Do not write it as $10-x$. We equated the two equations based on the fact that the output is the same work piece and not based on the effort.