Question

$15$ men can do a piece of work in $24$ days. In what time $10$ men can complete $\frac{1}{3}$ of the work.

Answer 1

Without any calculation put an arrow sign (head) towards unknown quantity and then calculate the arrow signs for other quantities.
While calculating arrow sign for men, consider that work done is not given.
Then think over that 15 men can do in 24 days, hence 10 men will take more time. Here number of men is decreasing but number of days is increasing.
$\therefore$ case is decrease-increase, arrow sign upwards.
But, while calculating arrow sign for work done consider that number of men is not given.
Then, think over that 1 work can be done in 24 days, hence in completing 1/3 of the work less number of days will be required, here the case is
Decrease-decrease, put the arrow sign downwards.
$\frac{x}{24}=\frac{15}{10}\times \frac{1/3}{1}$
$\therefore x=\frac{15}{10}\times \frac{1}{3}\times 24=12$ days