$A$ can do a certain work in $12$ days. $B$ is $60\%$ more efficient than $A$. How many days will $B$ and $A$ together take to do the same job?

$A$ can do a piece of work in $20$ days and $B$ in $30$ days. They work together for $7$ days and then both leave the work. Then $C$ alone finishes the remaining work in $10$ days. In how many days will $C$ finish the full work?

$6$ men or $12$ women can do a piece of work in $20$ days. In how many days can $8$ men and $16$ women do twice as big as this work?

$8$ men can complete a piece of work in $20$ days. $8$ women can complete the same work in $32$ days. In how many days will $5$ men and $8$ women together complete the same work?

$A$ takes three times as long as $B$ and $C$ together to do a job. $B$ takes four times as long as $A$ and $C$ together to do the work. If all the three,working together,can complete the job in $24$ days,then the number of days $A$ alone will take to finish the job is:

$A$ and $B$ can do a piece of work in $20$ days and $12$ days respectively. $A$ started the work alone and then after $4$ days $B$ joined him until the completion of the work. How long did the work last? (in days)