Register

CAT 2017 Set-2 | Question: 74

• retagged by
1,716 views
1 1 vote

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in $8$ hours. If the outlet pipe is open then the inlet pipe fills the empty tank in $10$ hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

  1. $20$
  2. $30$
  3. $40$
  4. $45$

1 Answer

1 1 vote
$\begin{array}{lcc} & \text{Inlet pipe (I)} & & \text{Outlet pipe + Inlet pipe (O+I)} \\ \text{Time:} & 8\;\text{hours} & & 10\;\text{hours} \\ \text{Total work:}  & \text{LCM}(8,10)  & = & 80\;\text{liters} \\ \text{(Capacity of tank)} & & & \\ \text{Efficiency:} & 10\;\text{liter/hour} & & 8\;\text{liter/hour}  \end{array}$

Now, $\text{I}_{\text{efficiency}} + \text{O}_{\text{efficiency}} = 8$

$\Rightarrow 10 + \text{O}_{\text{efficiency}} = 8$

$\Rightarrow \boxed{\text{O}_{\text{efficiency}} = -2}$

So,  $\text{Time} = \dfrac{\frac{\text{Capacity of tank}}{2}}{2}$         

$\Rightarrow \text{Time} = \dfrac{80}{4} = 20$ hours.

$\therefore$  If only the outlet pipe is open, then in $20$ hours the full tank becomes half-full.

Correct Answer$:\text{A}$
• edited by
Voting & Accepting an answer helps improve the community
← Previous · CAT 2017 Set-2 | Que...Next → · CAT 2017 Set-2 | Que...
← Previous in category · CAT 2017 Set-2 | Que...Next in category → · CAT 2017 Set-2 | Que...
Position:
Show:
Answer:

Related questions

1 1 vote
1 1 answer
2.0k
2.0k views
go_editor asked Mar 16, 2020
2,022 views
CAT 2017 Set-2 | Question: 79
Amal can complete a job in $10$ days and Bimal can complete it in $8$ days. Amal, Bimal and Kamal together complete the job in $4$ days and are paid a total amount of Rs ...
2 2 votes
1 answers 1 answer
2.9k
2.9k views
soujanyareddy13 asked Jan 20, 2022
2,865 views
CAT 2021 Set-2 | Quantitative Aptitude | Question: 20
Two pipes $\text{A}$ and $\text{B}$ are attached to an empty water tank. Pipe $\text{A}$ fills the tank while pipe $\text{B}$ drains it. If pipe $\text{A}$ is opened at $...
3 3 votes
1 1 answer
2.1k
2.1k views
go_editor asked Mar 20, 2020
2,120 views
CAT 2018 Set-2 | Question: 76
A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump $\text{A}$ or pump $\text{B}$ or both start working until the tank is full. On Monda...
2 2 votes
1 1 answer
2.0k
2.0k views
go_editor asked Mar 20, 2020
1,972 views
CAT 2018 Set-2 | Question: 78
A water tank has inlets of two types $\text{A}$ and $\text{B}$. All inlets of type $\text{A}$ when open, bring in water at the same rate. All inlets of type $\text{B}$, w...
2 2 votes
1 1 answer
2.4k
2.4k views
go_editor asked Mar 19, 2020
2,402 views
CAT 2018 Set-1 | Question: 68
A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty t...