$A$ can do a piece of work in $40$ days. He works at it for $8$ days and then, $B$ finishes it in $16$ days. How long will they take to complete the work if they do it together?

$A$ can do a piece of work in $18$ days, $B$ in$27$ days, $C$ in $36$ days. They start working together. But only $C$ works till the completion of work. $A$ leaves $4$days and $B$ leaves $6$ days before the completion of work. In how many days work will be completed?

$3$men and $4$ boys do a piece of work in $8 \mathrm{days}$, while $4$ men and $4$ boys finish it in $6 \mathrm{days}$. Then,$2$ men and $4$ boys will finish it in:

A contractor undertakes to complete work in $130$ days. He employs $150$ men for $25$ days and they complete $\frac{1}{4}$ of the work. He then reduces the number of men to $100,$ who work for $60$ days, after which there are $10$ days' holidays. How many men must be employed for the remaining period to finish the work?

Two pipes can fill a tank in $10 \mathrm{hours}$ and $15 \mathrm{hours}$ respectively. In how much time will they fill the tank when opened together?

Two pipes $\mathrm{A}$ and $\mathrm{B}$ can fill a cistern in $4 \mathrm{minutes}$ and $6 \mathrm{minutes}$, respectively. If these pipes are turned on alternately for $1 \mathrm{minute}$ each, how long will it take for the cistern to fill?