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?

$A$ can do a certain work in the same time in which $B$ and $C$ together can do it. If $A$ and $B$ together could do it in $10$ days and $C$ alone in $50$ days,then $B$ alone could do the work in (in days)

$P, Q$ and $R$ contract a work for $Rs. 550$. Together,$P$ and $Q$ are supposed to do $\frac{7}{11}$ of the work. How much does $R$ get? (in $Rs.$)

$P$ can do a piece of work in $9$ days. $Q$ is $50\%$ more efficient than $P$. The number of days it takes for $Q$ to do the same piece of work is

$6$ men can complete a piece of work in $12$ days. $8$ women can complete the same piece of work in $18$ days,whereas $15$ children can complete the piece of work in $10$ days. $4$ men,$12$ women,and $20$ children work together for $2$ days. If only men were to complete the remaining work in $1$ day,how many men would be required?

$X$ 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)