$10$ men can cut $15$ trees in $2$ hours. If $2$ men leave the job,how many trees will be cut in $3$ hours?

$P$ can do a piece of work in $9$ days. $Q$ is $50\%$ more efficient than $P$. The number of days it takes for $Q$ to do the same piece of work is

$A$ and $B$ working separately can do a piece of work in $9$ and $15 \, \text{days}$ respectively. If they work on alternate days beginning with $A$,then the work will be completed in how many days?

Ajay and Sunil together can complete a piece of work in $10$ days,Sunil and Sanjay in $15$ days,and Sanjay and Ajay in $20$ days. They worked together for $6$ days,and then Ajay leaves. Sunil and Sanjay worked together for $4$ more days,and Sunil leaves. How long will Sanjay take to complete the remaining work? (in days)

$8$ children and $12$ men complete a certain piece of work in $9$ days. If each child takes twice the time taken by a man to finish the work,in how many days will $12$ men finish the same work?

$20$ women together can complete a work in $16$ days. $16$ men together can complete the same work in $15$ days. The ratio of the working capacity of a man to that of a woman is