If a job is to be completed in $10 \, \text{days}$,it requires $270 \, \text{persons}$. If $180 \, \text{persons}$ take up the same job,they will finish it in (in $\text{days}$):

Ajay and Sunil together can complete a piece of work in $10$ days,Sunil and Sanjay in $15$ days,and Sanjay and Ajay in $20$ days. They worked together for $6$ days,and then Ajay leaves. Sunil and Sanjay worked together for $4$ more days,and Sunil leaves. How long will Sanjay take to complete the remaining work? (in days)

Two workers $A$ and $B$ working together completed a job in $5$ days. If $A$ worked twice as efficiently as he actually did and $B$ worked $\frac{1}{3}$ as efficiently as he actually did,the work would have completed in $3$ days. Find the time for $A$ to complete the job alone (in days).

$A$ and $B$ can do a piece of work in $12 \, \text{days}$ and $15 \, \text{days}$ respectively. They began to work together,but $A$ left after $4 \, \text{days}$. In how many more $days$ would $B$ alone complete the remaining work?

$A$ can do a work in $12$ days. When he had worked for $3$ days,$B$ joined him. If they complete the work in $3$ more days,in how many days can $B$ alone finish the work?

$A$ 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?