Question

$24$ workers working $6$ hours a day can finish a piece of work in $14$ days. If each worker works for $7$ hours a day, find the number of workers to finish the same piece of work in $8$ days.

Answer 1

Here we have 3 quantities i.e number of workers, number of hours per day and number of days.

No. of workers	No. of hours per day	No. of days
$24$	$6$	$14$
$?\left(x\right)$	$7$	$8$
$24:x$	$6:7$	$14:8=7:4$

\Number of workers inversely proportional to number of hours per day.
Number of workers $\propto$ $\frac{1}{numberofhoursperday}$
$24:x=$ inverse ratio of $6:7$ i.e, $7:6$
$\Rightarrow$ $24:x$ is directly proportional to $7:6$
Again, number of days is inversely proportional to number of workers.
Number of workers $\propto \frac{1}{numberofdays}$
$24:x=$ inverse ratio of $7:4$ i.e, $4:7$
As. number of workers depends upon two variables i.e number of days and number of hours per day. Therefore,
Number of workers $\propto$ compound ratio of inverse ratio of number of hours per day and inverse ration of number of days.
$24:x=$ compound ratio of $7:6$ and $4:7$
$24:x=7\times 4:6\times 7$
$24:x=4:6$
Product of means $=$ product of extremes
$2\times x=24\times 3$
$x=36$
Hence the required number of workers $=36$.