(B) Let the capacity of the cistern be the Least Common Multiple $(LCM)$ of $12, 15,$ and $20,$ which is $60$ units. Efficiency of the first tap = $6

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) Let the capacity of the cistern be the Least Common Multiple $(LCM)$ of $12, 15,$ and $20,$ which is $60$ units. Efficiency of the first tap = $60 / 12 = 5$ units/min. Efficiency of the second tap = $60 / 15 = 4$ units/min. When all pipes are open, the net efficiency = $60 / 20 = 3$ units/min. Let the efficiency of the waste pipe be $x$ units/min. Then, $5 + 4 - x = 3$. $9 - x = 3$, which gives $x = 6$ units/min. Time taken by the waste pipe to empty the full cistern = $\text{Total capacity} / \text{Efficiency of waste pipe} = 60 / 6 = 10$ minutes.

Competitive Quantitative Aptitude Pipes and Cistern Pipes and Cistern

Easy

$A$ cistern has two taps which fill it in $12$ $minutes$ and $15$ $minutes,$ respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in $20$ $minutes.$ How long will the waste pipe take to empty a full cistern?

A
$8 \text{ minutes}$
B
$10 \text{ minutes}$
C
$12 \text{ minutes}$
D
$16 \text{ minutes}$

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Pipes and Cistern

Subtopic

Pipes and Cistern

$12$ pumps working $6$ hours a day can empty a completely filled reservoir in $15$ days. How many such pumps working $9$ hours a day will empty the same reservoir in $12$ days?

Medium

View Solution

Two pipes can fill a cistern separately in $24$ $minutes$ and $40$ $minutes$ respectively. $A$ waste pipe can drain off $30 \text{ litres per minute}$. If all the three pipes are opened,the cistern fills in one $hour$. The capacity (in $litres$) of the cistern is:

Easy

View Solution

$A, B$ and $C$ are three pipes connected to a tank. $A$ and $B$ together fill the tank in $6$ $hrs$. $B$ and $C$ together fill the tank in $10$ $hrs$,and $C$ and $A$ together fill the tank in $7 \frac{1}{2}$ $hrs$. In how much time (in $hours$) will $A, B$ and $C$ fill the tank together?

Easy

View Solution

Two taps $A$ and $B$ can fill a water tank in $20$ $min$ and $24$ $min$ respectively,and a third tap $C$ empties the tank at a rate of $3$ $gallons$ per $min$. If all three taps $A$,$B$,and $C$ are opened together,the tank is filled in $15$ $min$. What is the capacity of the tank in $gallons$?

Medium

View Solution

$A$ pipe can fill a tank with thrice the speed of another pipe. If both the pipes together take $36$ $min$ to fill an empty tank completely,then how much time will it take for the slower pipe to fill the tank alone?

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ cistern has two taps which fill it in $12$ $minutes$ and $15$ $minutes,$ respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in $20$ $minutes.$ How long will the waste pipe take to empty a full cistern?

Similar Questions

$12$ pumps working $6$ hours a day can empty a completely filled reservoir in $15$ days. How many such pumps working $9$ hours a day will empty the same reservoir in $12$ days?

Two pipes can fill a cistern separately in $24$ $minutes$ and $40$ $minutes$ respectively. $A$ waste pipe can drain off $30 \text{ litres per minute}$. If all the three pipes are opened,the cistern fills in one $hour$. The capacity (in $litres$) of the cistern is:

$A, B$ and $C$ are three pipes connected to a tank. $A$ and $B$ together fill the tank in $6$ $hrs$. $B$ and $C$ together fill the tank in $10$ $hrs$,and $C$ and $A$ together fill the tank in $7 \frac{1}{2}$ $hrs$. In how much time (in $hours$) will $A, B$ and $C$ fill the tank together?

Two taps $A$ and $B$ can fill a water tank in $20$ $min$ and $24$ $min$ respectively,and a third tap $C$ empties the tank at a rate of $3$ $gallons$ per $min$. If all three taps $A$,$B$,and $C$ are opened together,the tank is filled in $15$ $min$. What is the capacity of the tank in $gallons$?

$A$ pipe can fill a tank with thrice the speed of another pipe. If both the pipes together take $36$ $min$ to fill an empty tank completely,then how much time will it take for the slower pipe to fill the tank alone?

Vedclass Test Series

Exam Paper Generator

Online Exam Module