$A$ can do a work in $20 \, \text{days}$ and $B$ in $40 \, \text{days}$. If they work on it together for $5 \, \text{days}$, then the fraction of the work that is left is:

Rohan and Mohit can build a wall in $8 \, days$,Mohit and Vikas can build the same wall in $10 \, days$,and Vikas and Rohan can build the same in $12 \, days$. In how many days can all three complete the same wall while working together?

$A$ can do a piece of work in $4 \, days$ and $B$ can do it in $12 \, days.$ In how many $days$ will they finish the work,both working together?

$10$ men and $15$ women together can complete a work in $6$ days. It takes $100$ days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

Raman is $25\%$ more efficient than Aman. If Aman can complete a piece of work in $25$ days,Raman can complete the same work in how many days?

If $A, B,$ and $C$ can complete a work in $6$ days together. If $A$ can work twice as fast as $B$ and thrice as fast as $C$,then the number of days $C$ alone can complete the work is (in days):