101

You visited us 101 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VII

Mathematics

Time and Work

A cistern has...

Question

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 the full cistern?

12

minutes

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10

minutes

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

8

minutes

No worries! We‘ve got your back. Try BYJU‘S free classes today!

16

minutes

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $10$ minutes
Let the waste pipe take $x$ minutes to empty the full cistern. Then,
$(\frac{1}{12} + \frac{1}{15} - \frac{1}{x}) = \frac{1}{20}$

$\Rightarrow \frac{1}{x} = \frac{1}{12} + \frac{1}{15} - \frac{1}{20} = \frac{5 + 4 - 3}{60} = \frac{6}{60} = \frac{1}{10}$

$∴$ The waste pipe takes 10 minutes to empty the full cistern.

Suggest Corrections

Similar questions

Q. A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened together in the empty tank, how much time will they take to fill the tank completely?

Two pipes P and Q would fill an empty cistern in 24 minutes and 32 minutes respectively. Both the pipes being opened together, find when the first pipe must be turned off so that the empty cistern may be just filled in 16 minutes.

Q. Two taps can separately fill a cistern in

10

minutes and

15

minutes, respectively and when the waste pipe is open, they can together fill it in

18

minutes. The waste pipe can empty the full cistern in:

Q. A cistern has two inlets

A

and

B

which can fill it in

12

minutes and

15

minutes respectively. An outer

C

can empty the full cistern in

10

minutes. If all the three pipes are opened together in the empty cistern, time taken to fill the cistern completely is _________.

Q. Two pipes

A

and

B

can separately fill a cistern in

60 m i n u t e s

and

75 m i n u t e s

respectively. There is a third pipe at the bottom of the cistern to empty it , If all the three pipes are simultancously opened, then the cistern is full in

50 m i n u t e s

, In how much time, the third pipe alone can empty the cistern ?

Join BYJU'S Learning Program

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 the full cistern?

The correct option is B 10 minutesLet the waste pipe take x minutes to empty the full cistern. Then, (112+115−1x)=120⇒1x=112+115−120=5+4−360=660=110∴ The waste pipe takes 10 minutes to empty the full cistern.

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 the full cistern?