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?

$A$ and $B$ complete a job in $12 \text{ days}$,while $A, B$,and $C$ can complete it in $8 \text{ days}$. $C$ alone will finish the job in (in $\text{days}$):

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

$A$ certain job was assigned to a group of men to do in $20$ days. But,$12$ men did not turn up for the job and the remaining men did the job in $32$ days. The original number of men in the group was:

Bansal,Gupta,and Singhal together can complete a work in $4 \, \text{days}$. If Bansal and Gupta together can complete the work in $4 \frac{4}{5} \, \text{days}$,and Gupta and Singhal together can do it in $8 \, \text{days}$,then Gupta alone can complete the work in (in $\text{days}$):

$A$ does half as much work as $B$ in $three-fourths$ of the time. If together they take $18$ days to complete a work,how much time shall $B$ take to do it alone? (in days)