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?

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 $\text{days}$):

$A$ contractor undertakes to dig a canal $12 \, km$ long in $350 \, days$ and employs $45$ men. After $200 \, days$ he finds that only $4.5 \, km$ of the canal has been completed. Find the number of extra men he must employ to finish the work in time (in $men$).

$A$ man,a woman,and a boy can complete a job in $3, 4,$ and $12$ days respectively. How many boys must assist $1$ man and $1$ woman to complete the job in $\frac{1}{4}$ of a day?

Two men,$A$ and $B$,working together,completed a piece of work. If worked individually,it would have taken them $30$ and $40$ days to complete the work. If they have received a payment of $Rs. 2100$,then $B$'s share is (in $Rs.$)

$A$ and $B$ working separately can do a piece of work in $9$ and $12$ days,respectively. If they work for a day alternately with $A$ beginning,the work would be completed in (in days):