Sarvesh K Verma Solutions for Chapter: Time and Work, Exercise 1: CAT - Test Questions Helping You Bell the CAT

Chandni and Divakar can do a piece of work in$9$ and $12$days, respectively. If they work for a day alternatively, Chandni beginning, then in how many days, the work will be completed?

Three typists $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ working together $8$ hours per day can type $900$ pages in $20$ days. In a day $\mathrm{B}$ types as many pages more than $\mathrm{A}$ as $\mathrm{C}$ types as many pages more than $\mathrm{B}$. The number of pages typed by $\mathrm{A}$ in $4$ hours equal to the number of pages typed by $\mathrm{C}$ in $1$ hour. How many pages $\mathrm{C}$ types in each hour?

Two pipes $\mathrm{A}$ and $\mathrm{B}$ can fill a tank in $24$ hours and $\frac{120}{7}$ hours respectively. Harihar opened the pipes $\mathrm{A}$ and $\mathrm{B}$ to fill an empty tank and some times later he closed the taps $\mathrm{A}$ and $\mathrm{B}$, when the tank was supposed to be full. After that it was found that the tank was emptied in $2.5$ hours because an outlet pipe $\mathrm{C}$ connected to the tank was open from the beginning. If Harihar closed the pipe $\mathrm{C}$ instead of closing pipes $\mathrm{A}$ and $\mathrm{B}$ the remaining tank would have been filled in :

Pipe $\mathrm{A}$ can fill a tank in $12$ hours and pipe $\mathrm{B}$ can fill it in $15$ hours, separately. $\mathrm{A}$ third pipe $\mathrm{C}$ can empty it in $20$ hours. Initially pipe $\mathrm{A}$ was opened, after one hour pipe $\mathrm{B}$ was opened and then after $1$ hour when pipe $\mathrm{B}$ was opened pipe $\mathrm{C}$ was also opened. In how many hours the tank will be - full?

Pipe $\mathrm{A}$ takes $3 / 4$ of the times required by pipe $\mathrm{B}$ to fill the empty tank individually. When an outlet pipe $\mathrm{C}$ is also opened simultaneously with pipe $\mathrm{A}$ and pipe $\mathrm{B}$, it takes $3 / 4$ more time to fill the empty tank than it takes, when only pipe $\mathrm{A}$ and pipe $\mathrm{B}$ are opened together. If it takes to fill $33$ hours when all the three pipes are opened simultaneously, then in what time pipe $\mathrm{C}$ can empty the full tank operating alone?

A tank has two inlet pipes which can fill the empty tank in $12$ hours and $15$ hours working alone and one outlet pipe which can empty the full tank in $8$ hours working alone. The inlet pipes are kept open for all the time but the outlet pipe was opened after $2$ hours for one hour and then again closed for $2$ hours then once again opened for one hour. This pattern of outlet pipe continued till the tank got completely filled. In how many hours the tank has been filled, working on the given pattern?

Working together, two pipes $\mathrm{A}$ and $\mathrm{B}$ can fill $7$ empty tanks of the same capacity in $48$ hours. When a tank was initially empty, pipe $\mathrm{B}$ was kept open for as much time as was required by pipe $\mathrm{A}$ to fill $1 / 3\mathrm{rd}$ of the empty tank by itself. Then, pipe $\mathrm{A}$ was kept open for as much time as was required by pipe $\mathrm{B}$ to fill up $1/4\mathrm{th}$ of the empty tank by itself. It was then found that the tank was $7/12$ full. The least time in which any of the pipes can fill an empty tank fully is

Ram Lal is a renowned packager of fruits in Varanasi. He packs $70$ mangoes or $56$ guavas every day working $7$ hours per day. His wife also helps him. She packs $30$ mangoes or $24$ guavas working $6$ hours per day. Ram Lal has to pack $3300$ mangoes and $2400$ guavas with the help of his wife. They work alternatively, each day $10$ hours. His wife started packaging on the first day and works on every alternate days. Similarly Ram Lal started his work on second day and worked alternatively till the completion of the work. In how many days the work will be finished?