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Q:

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

A) 10 B) 12
C) 14 D) 16

Answer:   C) 14

Explanation:

Part filled in 2 hours ={\color{Black} \frac{2}{6}=\frac{1}{3}}

Remaining part ={\color{Black} \left ( 1-\frac{1}{3} \right )=\frac{2}{3}}

{\color{Black} \therefore } (A + B)'s 7 hour's work ={\color{Black} \frac{2}{3}}

(A + B)'s 1 hour's work ={\color{Black} \frac{2}{21}}

{\color{Black} }{\color{Black}\therefore }C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

={\color{Black} \left ( \frac{1}{6}-\frac{2}{21} \right )=\frac{1}{14}}

{\color{Black} \therefore }C alone can fill the tank in 14 hours.

Q:

A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half ?

A) 31 min B) 29 min
C) 28 min D) 30 min
 
Answer & Explanation Answer: D) 30 min

Explanation:

Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
(x/2) x (1/15) = 1 => x = 30 min.

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Q:

A tank is filled in eight hours by three pipes K, L and M. Pipe K is twice as fast as pipe L, and L is twice as fast as M. How much time will pipe L alone take to fill the tank ?

A) 32 hrs B) 24 hrs
C) 28 hrs D) 26 hrs
 
Answer & Explanation Answer: C) 28 hrs

Explanation:

1/K + 1/L + 1/M = 1/8 (Given)
Also given that K = 2L and L = 2M
=> 1/2L + 1/L + 2/L = 1/8
=> (1 + 2 + 4)/2L = 1/8
=> 2L/7 = 8
=> L = 28 hours.

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1 19
Q:

Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank ?

A) 15 min 20 sec. B) 16 min 40 sec.
C) 13 min 10 sec. D) 14 min 40 sec.
 
Answer & Explanation Answer: D) 14 min 40 sec.

Explanation:

Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15

Remaining part = 1 - 7/15 = 8/15

Part filled by B in 1 minute = 1/20

1/20 : 8/15 :: 1 : k

k = 8/15 x 1 x 20 = 10 2/3 min = 10 min 40 sec.

The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.

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Q:

Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 3 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill  ?

A) 8.21 min B) 8 min
C) 8.57 min D) 8.49 min
 
Answer & Explanation Answer: C) 8.57 min

Explanation:

1/10 + 1/15 = 1/6 x 3 = 1/2

1 - 1/2 = 1/2

1/10 + 1/15 - 1/x = 1/2

x = 8.57 min

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Q:

Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes  ?

A) 21 min B) 24 min
C) 20 min D) 22 min
 
Answer & Explanation Answer: A) 21 min

Explanation:

Let the pipe B be closed after 'K' minutes.

30/16 - K/24 = 1 => K/24 = 30/16 - 1 = 14/16

=> K = 14/16 x 24 = 21 min.

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