$P$ and $Q$ complete a certain work in $30 \, days$,$Q$ and $R$ in $40 \, days$,while $R$ and $P$ in $60 \, days$. How long will they take to finish it together? (in $days$)

$A$ and $B$ can complete a piece of work in $45$ and $40$ days,respectively. They began the work together,but $A$ leaves after some days and $B$ completed the remaining work in $23$ days. After how many days did $A$ leave?

Bansal,Gupta,and Singhal together can complete a work in $4 \, \text{days}$. If Bansal and Gupta together can complete the work in $4 \frac{4}{5} \, \text{days}$,and Gupta and Singhal together can do it in $8 \, \text{days}$,then Gupta alone can complete the work in (in $\text{days}$):

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 $Rs.$)

$A$ and $B$ together can complete a work in $30$ days. They started together but after $6$ days $A$ left the work and the work is completed by $B$ after $36$ more days. $A$ alone can complete the entire work in how many days?

$40$ men can complete a work in $40$ days. They started the work together. But at the end of each $10^{th}$ day,$5$ men left the job. The work would have been completed in (in days):