$A$ 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?

If a work can be completed by $A$ in $30 \text{ days}$ and by $B$ in $60 \text{ days}$,then the number of days taken by them to finish the work,working together,is

$A$ and $B$,working together,can complete a piece of work in $12$ days. $B$ and $C$ working together can complete the same piece of work in $16$ days. $A$ worked at it for $5$ days and $B$ worked at it for $7$ days. $C$ finished the remaining work in $13$ days. How many days would $C$ alone take to complete it?

$A$ takes twice as much time as $B$ or thrice as much time as $C$ to finish a piece of work. Working together,they can finish the work in $2$ days. $B$ can do the work alone in (in days):

$5$ men can prepare $10$ toys in $6$ days working $6$ hours a day. Then,in how many days can $12$ men prepare $16$ toys working $8$ hours a day? (in days)

Sister can bake $50$ cakes in $25$ hours. Sister and Mummy together can bake $75$ cakes in $15$ hours. How many cakes can Mummy bake in $15$ hours?