Facts Of Time and Work

Time and work relate to indirect proportion. An increase in one quantity leads to a decrease in the other quantity and vice versa. The more hours people work, the less time it takes to complete the same amount of work. Conversely, the fewer men to work on a particular task, the more time will be taken to complete the job.

Example 1: If 30 workers can build a wall in 24 hours, how many workers will be required to do the same work in 18 hours?

Solution: Let the number of workers be \(x\).

\(
\begin{array}{|c|c|c|}
\hline \text { Number of Hours } & 24 & 18 \\
\hline \text { Number of Workers } & 30 & x \\
\hline
\end{array}
\)
We know that the more the number of workers, the lesser time will be taken to complete the same amount of work.
Therefore, the number of hours and the number of workers are in inverse proportion.
So, \(30 \times 24=x \times 18\)
Thus, \(x=\frac{30 \times 24}{18}=40\) Hence, to finish the work in 18 hours, 40 workers will be required.

Example 2: It takes 42 days for Ashok to construct a \(12 \mathrm{~m}\) long wall. How long will it take him to complete a \(20 \mathrm{~m}\) long wall?

Solution: Time required to construct \(12 \mathrm{~m}\) long wall \(=42\) days
Time required to construct \(1 \mathrm{~m}\) long wall \(=\frac{42}{12}\) days
Therefore, time required to construct \(20 \mathrm{~m}\) long wall \(=\frac{42}{12} \times 20=70\) days. Hence, it will take 70 days for Ashok to complete \(20 \mathrm{~m}\) long wall.

Example 3: If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 20 hours?

Solution:

Let the number of workers be \(x\).
\(
\begin{array}{|l|c|c|}
\hline \text { Number of Hours } & 48 & 20 \\
\hline \text { Number of Workers } & 15 & {x} \\
\hline
\end{array}
\)
We know that the more the number of workers, the lesser time will be taken to complete the same amount of work. Therefore, the number of hours and the number of workers are in inverse proportion.
So, \(15 \times 48=x \times 20\)
Thus, \(x=\frac{15 \times 48}{20}=36\) Hence, to finish the work in 20 hours, 36 workers will be required.