Monica Capoor Solutions for Chapter: Time and Work, Exercise 2: EXERCISE

Rani can complete $\frac{1}{5}$ of a work in $6$ days and Sudarshan can complete $\frac{1}{4}$ of the same work in $5$ days. How long will both of them take to complete that work if they work together$?$

$\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ working together can finish a piece of work in $4$ hours. $\mathrm{A}$ alone can do it in $12$ hours and $\mathrm{B}$ alone can do it in $10$ hours, In how many hours will $\mathrm{C}$ alone do the same work$?$

$\mathrm{A}$ and $\mathrm{B}$ can do a piece of work in $10$ days, $\mathrm{B}$ and $\mathrm{C}$ in $15$ days and $\mathrm{C}$ and $\mathrm{A}$ in $12$ days. In how many days can $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ finish it if they all work together$?$ Also find the number of days $\mathrm{B}$ will require to finish the work if he works alone.

$\mathrm{A}$ can do a piece of work in $12$ days and $\mathrm{B}$ can do in $18$ days. They worked together for $4$ days when $\mathrm{A}$ fell ill and $\mathrm{B}$ had to complete the remaining work. In how many days was the work completed $?$

Two inlet pipes $\mathrm{A}$ and $\mathrm{B}$ can fill an empty cistern in $4$ hours and $8$ hours, respectively. If both are opened together in the empty cistern, how much time will they take to fill it completely$?$

Tap $\mathrm{A}$ can fill an empty cistern in $4$ hours while the outlet pipe $\mathrm{B}$ can empty it in $6$ hours. How long will it take to fill the cistern if both the tap and the pipe are opened simultaneously$?$

Three taps $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ can fill an empty water tank in $12$ hours, $16$ hours and $24$ hours, respectively. How long would the three taps take to fill the empty water tank if all of them are opened simultaneously$?$

A cistern has two inlet pipes $\mathrm{A}$ and $\mathrm{B}$ which can fill it in $8$ hours and $6$ hours, respectively. An outlet pipe $\mathrm{C}$ can empty the full cistern in $4$ hours. If the pipes $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are opened simultaneously in the empty cistern, how much time will they take to fill the cistern completely$?$