Question

A group of workers can do a piece of work in $24$ days. However as $7$ of them were absent it took $30$ days to complete work. How many people actually worked on the job to complete it?

• A. $28$
• B. $35$
• C. $30$
• D. $42$

Answer 1

The correct option is A $28$

Let the original number of workers in the group be "$x$"
therefore, actual number of workers $=x-7$.
We know that the number of man hours required to do the job is the same in both the cases.
Therefore, $x\left(\begin{array}{c}24\end{array}\right)=\left(\begin{array}{c}x-7\end{array}\right).30$
$⟹24x=30x-210$
$⟹6x=210$
$⟹x=35$.
Therefore, the actual number of workers who worked to complete the job $=x-7=35-7=28$.