PRACTICE QUESTIONS CLASSROOM WING

$\mathrm{X}, \mathrm{Y} \mathrm{and} \mathrm{Z}$ can complete a piece of work in $10 \mathrm{days}$. $\mathrm{X} \mathrm{and} \mathrm{Y}$ can do it in $20 \mathrm{days}$. Then $\mathrm{Z}$ alone can complete the work in _____ $\mathrm{days}$.

Satish can do $\frac{1}{5}\mathrm{th}$ of a work in $5$ $\mathrm{days}$, whereas he and Ramesh together can do $\frac{9}{5}\mathrm{th}$ of the same work in $10$ $\mathrm{days}$. They start the work together and work for $5$ $\mathrm{days}$ after which Satish leaves. Find the number of days in which Ramesh alone can finish the remaining work.(In $\mathrm{days}$).

$\mathrm{A}$ and $\mathrm{B}$ together can do a piece of work in $20$ $\mathrm{days}$, whereas $\mathrm{B}$ and $\mathrm{C}$ together can do the same work in $15$ $\mathrm{days}$. If $\mathrm{A}$,$\mathrm{B}$ and $\mathrm{C}$ together can finish this work in $10$ $\mathrm{days}$, then find the number of days in which $\mathrm{B}$ alone can finish the work.(in $\mathrm{days}$).

Three pipes $\mathrm{X},$ $\mathrm{Y}$, and $\mathrm{Z}$  can fill a tank in $120$ $\mathrm{minutes}$. Pipe $\mathrm{X}$ is twice faster than pipe$\mathrm{Y}$, pipe $\mathrm{Y}$ is thrice faster than pipe $\mathrm{Z}$. In how many hours can pipe $\mathrm{Z}$ fill the tank ?

$4$ women and $3$ men can do a piece of work in $2$ $\mathrm{days}$, whereas $6$ women and $2$ men can also finish it in $2$$\mathrm{days}$. Now, find the time taken by one woman to complete the same job working alone. Also, find the time one man takes to complete the same job working alone.
 

$\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ can do a work in $20$,$45$ and $120$ $\mathrm{days}$, respectively. They started the work. $\mathrm{A}$ left $10$ $\mathrm{days}$ before and $\mathrm{B}$ left  $5$ $\mathrm{days}$ before the completion of work. In how many days is the total work completed?(in $\mathrm{days}$).

Two pipes $\mathrm{P}$ and $\mathrm{Q}$ can fill a cistern in $15$$\min$and $20$ $\min$, respectively. Both are opened together, but at the end of $5$ $\min$,  the pipe $\mathrm{P}$ is turned off. How long will the pipe $\mathrm{Q}$ take to fill the cistern?

$\mathrm{A}$ and $\mathrm{B}$ can do a piece of work in $12$ $\mathrm{days}$, $\mathrm{B}$ and $\mathrm{C}$ in $15$ $\mathrm{days}$ and $\mathrm{C}$ and $\mathrm{A}$ in $20$ $\mathrm{days}$. In how many days can they do it, all working together?