1. Pipes A and B can fill a cistern in 6 hrs. and 8 hrs. respectively. If both the pipes are opened simultaneously when will the tank be filled?
a) 3 hrs. b) 7 hrs. c) 20/7 hrs. d) 24/7 hrs.
Answer:
Pipe A can fill the tank in 6 hrs. ⇒ A’s rate of work per hour = 1/6 Pipe B can fill the tank in 8 hrs. ⇒ B’s rate of work per hour = 1/8
Both the pipes are opened simultaneously,
Its rate of work = 1/6 + 1/8 = 7/24
The tank will be filled in 24/7 hrs. So, the answer is (d)
2. First 2 pipes can fill a cistern in 5 hours and 6 hours respectively while the 3rd pipe can empty the tank in 10 hrs. if all the 3 pipes are opened simultaneously, in how many hours the tank will be filled?
a) 3 hrs. 20 min b) 3 hrs. 40 min. c) 4 hrs. 10 min. d)
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⇒ Its rate of work = 1/4 So, n pipes rate of work = n/4
Likewise,
Each drained pipes take 3 hrs. to empty the tank ⇒ Its rate of work = 1/6 So, (4 – n) pipes rate of work = (4-n)/6 While all the 4 pipes are opened, 1/6th of the tank can be drained in an hour. i.e., n/4 - (4-n)/6 = 1/6 ⇒ (3n – 8 + 2n)/12 = 1/6 ⇒ (5n – 8) = 2 ⇒ 5n =10 ⇒ n = 2
So, the answer is (a)
4. Pipe A fills a tank in 4 hrs. Because of a leak at the bottom of the tank, it takes pipe A 60 min. more to fill the tank. If pipe A is shut then how long the leak takes to empty the full tank?
a) 15 hrs. b) 10 hrs. c) 20 hrs. d) 12 hrs.
Answer:
Pipe A fills a tank in 4 hrs. ⇒ Its rate of work per hour = 1/4
Let us take the time taken for leakage when A is shut is x hrs.
So, the rate of work for the leakage is 1/x per hour.
Because of a leak the time taken to fill the tank = 4 hrs. + 60 min = 5 hrs.
i.e., 1/4 – 1/x = 1/5
1/x = 1/4 – 1/5 = 1/20 ⇒ x = 20 So, the answer is (c)
5. Two taps A and B can fill a tub in 24 min. and 30 min respectively. If both are opened simultaneously and B is closed after 6 min. then how long would A alone take to fill the tub?
a) 18 min. 36 sec b) 12 min. 36 sec c) 10 min. 36 sec. d) 20 min. 36
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A large fresh water reservoir can be filled by two pipes S and T in 30 min and 20 min respectively. How many minutes will be taken to fill the reservoir if T is used for ½ the time and S and T fill it together for the remaining half?
a) 10 min b) 12 min c) 15 min d) 20 min
10. A bucket can fill a drum in 12 hrs. After ½ the drum is filled, 3 more similar buckets are turned. The total time taken to fill the tank completely is:
a) 2 hrs b) 3 hrs c) 4 hrs d) 5 hrs
11. Pipes A, B and C can fill a cistern in 12, 15 and 20 hrs respectively. If A is open all the time and B and C are open for one hour each alternatively, then when will the cistern be filled?
a) 6 hrs b) 5 hrs c) 4 hrs d) 7 hrs
12. A tank can be filled in 8 hrs but due to the leakage at the bottom of the tank it takes 12 hrs to fill the tank. If the tank is full, then how long it will take to empty the tank?
a) 48 hrs b) 96 hrs c) 89 hrs d) 53 hrs
13. A drum can be filled by a bucket in 40 min and by another bucket in 120 min. both the buckets are filled simultaneously for 20 min and then the 1st bucket is shut off. After this, when will the drum be filled completely?
a) 20 min b) 30 min c) 40 min d) 50