$12$ men complete a work in $9$ days. After they have worked for $6$ days,$6$ more men join them. How many days will they take to complete the remaining work?

Nikita,Nishita,and Kavita can complete a work in $2 \frac{2}{3}$ days. If Nishita and Kavita can complete it in $4$ days,and Nishita alone can do it in $6$ days,then in how many days can Nikita and Nishita complete the work?

Ram,Rajan,and Rangan can do a certain work in $6, 12,$ and $24$ days respectively. In what time will they altogether do it? (in days)

If $A$ works alone,he would take $4$ days more to complete the job than if both $A$ and $B$ worked together. If $B$ worked alone,he would take $16$ days more to complete the job than if $A$ and $B$ work together. How many days would they take to complete the work if both of them worked together?

$A, B$ and $C$ can do a job in $6$ days,$12$ days and $15$ days,respectively. After $\frac{1}{8}$ of the work is completed,$C$ leaves the job. The rest of the work is done by $A$ and $B$ together. The total time taken to finish the work is (in days):

$A$ and $B$ working separately can do a piece of work in $10 \text{ days}$ and $15 \text{ days}$ respectively. If they work on alternate days beginning with $A$,in how many days will the work be completed?