Question

A man can complete his work in $24$ days by working $5$ hours a day. How many days will he take to complete the same work; working $8$ hours a day?

Answer 1

Hint: A man can complete his work in $24$ days by working $5$ hours a day and we have to find that how many days will it take if he works $8$ hours a day, so the number of hours worked and the number of days taken are in inverse proportion. Try it you will definitely get an answer.

Complete step-by-step answer:
If the man works for more hours a day, it will take less number of days to finish the work.
Hence, the number of hours worked and the number of days taken are in inverse proportion.
Let the number of days taken do the work, if the man worked for $8$ hours a day be $a$.
So using inverse proportion we get,
$24:a=$inverse ratio of $5:8$
$24:a=8:5$
Applying the rule, product of extremes$=$product of means.
 $24\times 5=a\times 8$
Simplifying in simple manner we get,
$a=\dfrac{24\times 5}{8}$
$a=15$
Hence, the man will take $15$ days to do the work, if he works $8$ hours a day.

Additional information:
A direct and inverse proportion are used to show how the quantities and amounts are related to each other. They are also mentioned as directly proportional or inversely proportional. The symbol used to denote the proportionality is $\alpha $. For example, if we say, $a$ is proportional to $b$, then it is represented as $a\alpha b$ and if we say, $a$ is inversely proportional to $b$, then it is denoted as ‘$a\alpha \dfrac{1}{b}$’. These relations are governed by some proportionality rules. Now in both cases, the value of ‘$a$’ changes in terms of ‘$b$’ or when the value of ‘$b$’ changes, the value of ‘$a$’ also changes. The change in both values is equated with a constant of proportionality. Basically, a proportion states that two ratios like $\dfrac{a}{b}$ and $\dfrac{c}{d}$ are equal to each other, in such a way, $\dfrac{a}{b}=\dfrac{c}{d}$.

Note: Keep in mind that If the man works for more hours a day, it will take less number of days to finish the work. Here, the number of hours worked and the number of days taken are in inverse proportion. Also, we have used the inverse proportion concept.