$A$ and $B$ can complete a piece of work in $18$ days; $B$ and $C$ in $24$ days; $C$ and $A$ in $36$ days. $A$ alone can complete the work in (in days):

The total number of men,women,and children working in a factory is $18$. They earn $Rs. 4000$ in a day. If the sum of the wages of all men,all women,and all children is in the ratio $18: 10: 12$,and the wages of an individual man,woman,and child are in the ratio $6: 5: 3$,then how much does a woman earn in a day? (in $Rs.$)

$A$ can complete a work in $10$ days,$B$ can complete the same work in $20$ days,and $C$ in $40$ days. $A$ starts working on the first day,$B$ works on the second day,and $C$ works on the third day. Again,$A$ works on the fourth day,$B$ on the fifth day,and so on. If they continue working in the same way,in how many days will the work be completed?

$A$ can complete a piece of work in $40$ days. He starts working,but having some other engagements,he leaves after $5$ days. Thereafter,$B$ completes the remaining work in $21$ days. How many days would $A$ and $B$ take to complete this work working together?

$A$ tyre has two punctures. The first puncture alone would have made the tyre flat in $9 \,minutes$ and the second alone would have done it in $6 \,minutes.$ If air leaks out at a constant rate,how long does it take both the punctures together to make it flat? (in $minutes$)

$A$ is thrice as good a workman as $B$,therefore,$A$ is able to finish a piece of work in $60 \, days$ less than $B$. The time (in $days$) in which they can do it working together is