Raj and Ram working together can do a piece of work in $10 \text{ days}$. Raj alone can do it in $12 \text{ days}$. In how many days will Ram alone do the work?

$A$ man is twice as fast as a woman and a woman is twice as fast as a boy in doing a work. If all of them, a man, a woman and a boy, can finish the work in $7$ days, in how many days will a boy do it alone?

$A$ is $30\%$ more efficient than $B.$ How much time will they,working together,take to complete a job which $A$ alone could have done in $23$ days? (in days)

$A$ can complete a work in $m$ days and $B$ can complete it in $n$ days. How many days will it take to complete the work if both $A$ and $B$ work together?

$P$ and $Q$ together can do a job in $6$ days. $Q$ and $R$ can finish the same job in $60/7$ days. $P$ started the work and worked for $3$ days. $Q$ and $R$ continued for $6$ days. Then the difference of days in which $R$ and $P$ can complete the job is

$A$ and $B$ can do a piece of work in $18$ days,$B$ and $C$ in $24$ days,and $A$ and $C$ in $36$ days. In what time can they do it all working together? (in days)