Aptitude :: Pipe And CisternPage 2

9.

Tap P can fill a tank in 3 hours and tap Q can fill the tank in 4 hours. What fraction of the tank can be filled by tap P alone in the time taken by both working together to fill the tank?
(a)3/7
(b)2/7
(c)1/7
(d)4/7
Answer is: DRatio of efficiencies of P and Q is = 1/3 : 1/4 i. e. 4 : 3
∴ In the time the tank is filled completely by both taps working together tap P can fill (4/7)th of the tank.
Note: Here, the actual time taken to fill the tank is not required.

10.

A certain number of taps filled a tank in 7 hours. If there were 4 taps less, the tank would have been filled in 11 hours. Find the number of taps?
(a)7
(b)11
(c)13
(d)14
Answer is: BThe number of taps is inversely proportional to the time taken.
The less the taps, the more the time taken.
Ratio of times taken = 7 : 11
Ratio of number of taps = 11 : 7
Let the number of taps be 11X and 7X.
⇒11X – 7X = 4
⇒X = 1
Hence, Number of taps = 11

11.

Two taps A and B can fill a tank in 20 min and 30 min respectively. If both the taps are opened simultaneously and tap A is closed after 5 min, what is the total time in which the tank is filled?
(a)14.5 min
(b)20 min
(c)22.5 min
(d)25 min
Answer is: CA and B can fill (1/20)th and (1/30)th the tank in 1 min.
In 5 min they fill 5 x (1/20 + 1/30) = 5 x (3 + 2)/60 = (5/12)th of the tank.
The rest (7/12)th is filled by B in (7/12) x 30 = 17.5 min.
Time taken to fill the tank is (5 + 17.5) = 22.5 min.

12.

Three taps can fill a tank in 10, 15 and 30 hours. If each tap is opened for one hour one after the other till the tank gets full, how long does it take to fill the tank?
(a)20 hours
(b)18 hours
(c)12 hours
(d)15 hours
Answer is: DIn three hours each tap is opened once.
Therefore in three hours 1/10 + 1/15 + 1/30 = (1/5)th of the tank is filled.
∴ The time is full in 5 x 3 = 15 hours.

13.

A water tank is two-fifth full. Pipe A can fill a tank in 10 min and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(a)6 min. to empty
(b)6 min. to fill
(c)9 min. to empty
(d)9 min. to fill
Answer is: AClearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/6 – 1/10) = 1/15.
∴ [1/15 : 2/5]∷[ 1 : X]
X = (2/5 x 1 x 15) = 6 min.
So, the tank will be emptied in 6 min.

14.

Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
(a)2 hours.
(b)2.5 hours.
(c)3 hours.
(d)3.5 hours.
Answer is: CPart filled by (A + B + C) in 1 hour = (1/5 + 1/10 + 1/30) = 1/3
∴ All the three pipes together will fill the tank in 3 hours.

15.

Two pipes A and B can separately fill a cistern in 60 min. and 75 min. respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time the third pipe alone can empty the cistern?
(a)90 min.
(b)100 min.
(c)110 min.
(d)120 min.
Answer is: BWork done by the third pipe In 1 min. = 1/50 – (1/60 + 1/75)
Work done by the third pipe In 1 min. = (1/50 – 3/100) = - 1/100
[- ve sign means emptying].
∴ The third pipe alone can empty the cistern in 100 min.

16.

A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(a)20 hours
(b)25 hours
(c)35 hours
(d)CBD
Answer is: CSuppose pipe A alone takes X hours to fill the tank.
Then, pipes B and C will take X/2 and X/4 hours respectively to fill the tank.
∴ 1/X + 2/X + 4/X = 1/5
⇒ 7/X = 1/5
⇒ X = 35 hrs.

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