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

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 $a$

Then, $24:a::$ inverse ratio of $5:8$
$=>24:a=8:5$

Applying the rule, product of extremes $=$ product of means

$24\times 5=a\times 8$

$a=\frac{24\times 5}{8}$

$a=15$
Hence, the man will take $15$ days to do the work, if he works $8$ hours a day.