$A$ 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?

If $3$ men and $4$ boys can earn $Rs. 2100$ in $7$ days,and $11$ men and $13$ boys can earn $Rs. 8300$ in $8$ days,in what time will $7$ men and $9$ boys earn $Rs. 11000$? (in days)

$A$ 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?

Akka can bake $100$ cakes in $20$ hours. Akka and Tai together can bake $75$ cakes in $10$ hours. How many cakes can Tai bake in $20$ hours?

Hemant decided to build a farmhouse in $40$ days. He employed $100$ men in the beginning and $100$ more after $35$ days and completed the construction in the stipulated time. If he had not employed the additional men,how many days behind schedule would it have been finished? (in days)

$A$ can do a job in $6 \, days$ and $A$ and $B$ can do it together in $2 \, days.$ How many $days$ will be taken by $B$ to do the job alone?