$P$,$Q$ and $R$ contracted to do a work for $Rs. 4200$. $P$ can do the work in $6$ days,$Q$ in $10$ days and $R$ in $12$ days. If they work together to do the work,what is the share of $R$ (in $Rs.$)?

$A$ can finish a work in $18$ days and $B$ can do the same work in half the time taken by $A$. Then,working together,what part of the same work can they finish in a day?

$A$ is $20\%$ more efficient than $B$. If $B$ alone can complete a piece of work in $12$ days,then $A$ alone can complete the same work in how many days?

$A$ certain number of persons can complete a piece of work in $55 \text{ days}$. If there were $6$ persons more,the work could be finished in $11 \text{ days}$ less. How many persons were originally there?

Ramesh takes twice as much time as Mahesh and thrice as much time as Suresh to complete a job. If working together,they can complete the job in $4 \, \text{days}$,then the time taken by each of them separately to complete the work is (in $\text{days}$)

$A$ can do $\frac{1}{3}$ of a work in $5 \text{ days}$ and $B$ can do $\frac{2}{5}$ of the work in $10 \text{ days}$. In how many $\text{days}$ can both $A$ and $B$ together do the work?