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All Free Mathematics MCQs with Answers

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1,551 questions · page 64 of 78

1261. 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
  • B. 2.5
  • C. 3
  • D. 3.5

Explanation: The combined filling rate is 1/5 + 1/10 + 1/30 = 10/30 = 1/3 tank/hour. Therefore, the tank is filled in 1 ÷ 1/3 = 3 hours.

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Correct answer: 3

1262. A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes 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 full
  • C. 9 min. to empty
  • D. 9 min. to full

Explanation: The filling rate is 1/10 tank/minute and the emptying rate is 1/6 tank/minute, so the net emptying rate is 1/6 - 1/10 = 1/15 tank/minute.

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Correct answer: 6 min. to empty

1263. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

  • A. 12 min
  • B. 15 min
  • C. 25 min
  • D. 50 min

Explanation: The two pipes supply 1/20 + 1/30 = 3/60 + 2/60 = 1/12 tank per minute. Thus, working together, they fill the tank in 12 minutes.

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Correct answer: 12 min

1264. A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?

  • A. 24 hours
  • B. 28 hours
  • C. 32 hours
  • D. 36 hours

Explanation: Let C's rate be x tank/hour. Then B's rate is 2x and A's rate is 4x, so the total rate is 7x = 1/8 tank/hour; hence B's rate is 2/56 =…

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Correct answer: 28 hours

1265. Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?

  • A. 16 hours
  • B. 15 hours
  • C. 18 hours
  • D. 17 hours

Explanation: Pipe A's rate is 1/6 tank/hour, but its net rate with the leak is 1/9 tank/hour.

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Correct answer: 18 hours

1266. 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. 20
  • B. 24
  • C. 23
  • D. None of these

Explanation: During the first t minutes, the net rate is 1/16 - 1/24 = 1/48 tank/minute; after B closes, A supplies at 1/16 tank/minute for 30 - t…

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Correct answer: None of these

1267. Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?

  • A. 12
  • B. 13
  • C. 11
  • D. 10

Explanation: The two inlet pipes and the outlet have a net rate of 1/18 + 1/15 - 1/45 = 5/90 + 6/90 - 2/90 = 1/10 tank/minute.

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Correct answer: 10

1268. Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in___________?

  • A. 17 hours
  • B. 12 hours
  • C. 16 hours
  • D. 24 hours

Explanation: Three equal pipes fill 1 tank in 8 hours, so their combined rate is 1/8 tank/hour.

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Correct answer: 12 hours

1269. A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?

  • A. 3 PM
  • B. 7 PM
  • C. 4 PM
  • D. 5 PM

Explanation: From 1 to 2 AM, A fills 1/4 tank; from 2 to 3 AM, A and B fill 1/4 + 1/5 = 9/20 tank, leaving 7/10 tank.

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Correct answer: 5 PM

1270. Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?

  • A. 6 min
  • B. 12 min
  • C. 19 min
  • D. 10 min

Explanation: Assuming A is opened first, in each 2-minute cycle the pipes fill 1/8 + 1/24 = 1/6 tank, so 10 minutes fills 5/6 tank.

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Correct answer: 12 min

1271. A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?

  • A. 60 min
  • B. 80 min
  • C. 70 min
  • D. 48 min

Explanation: The filling pipe supplies 1/20 tank/minute and the leak removes 1/28 tank/minute.

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Correct answer: 70 min

1272. A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?

  • A. 45 hrs
  • B. 60 hrs
  • C. 75 hrs
  • D. 90 hrs

Explanation: Without the leak, the filling rate is 1/9 tank/hour, while with the leak the net rate is 1/10 tank/hour.

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Correct answer: 90 hrs

1273. pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes?

  • A. after 12 mins
  • B. after 9 mins
  • C. after 8 1/2 mins
  • D. after 10 mins

Explanation: Pipe Q remains open for all 12 minutes and supplies 12/24 = 1/2 tank. Pipe P must supply the remaining 1/2 tank, so its operating time is…

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Correct answer: after 9 mins

1274. Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?

  • A. 25 hrs
  • B. 28 hrs
  • C. 20 hrs
  • D. 35 hrs

Explanation: Let the faster pipe take x hours, so the slower pipe takes x + 10 hours.

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Correct answer: 20 hrs

1275. An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?

  • A. 4/9
  • B. 2/3
  • C. 4/7
  • D. 1/6

Explanation: The outlet empties 2/3 of the cistern in 12 minutes, so its rate is (2/3) ÷ 12 = 1/18 of the cistern per minute.

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Correct answer: 4/9

1276. A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?

  • A. 5260 liters
  • B. 5760 liters
  • C. 5846 liters
  • D. 6970 litersAccessing Digital Reference Tools

Explanation: If the tank capacity is C litres, the leak empties C/6 litres per hour.

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Correct answer: 5760 liters

1277. Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?

  • A. 480 liters
  • B. 540 liters
  • C. 600 liters
  • D. 675 liters

Explanation: The two filling pipes together work at 1/12 + 1/15 = 3/20 of the tank per minute.

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Correct answer: 540 liters

1278. Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?

  • A. 3 1/4 min
  • B. 5 1/4 min
  • C. 8 1/4 min
  • D. 9 1/4 min

Explanation: In the first 3 minutes, A and B fill 3 x (1/12 + 1/15) = 3 x 3/20 = 9/20 of the cistern.

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Correct answer: 8 1/4 min

1279. Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?

  • A. 2 hrs 15 min
  • B. 4 hrs 24 min
  • C. 5 hrs
  • D. 3 hrs

Explanation: In each two-hour cycle, pipe A fills 1/4 of the tank and pipe B fills 1/5, so together they fill 9/20 in 2 hours.

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Correct answer: 4 hrs 24 min

1280. Two taps can separately fill a cistern 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?

  • A. 7 min
  • B. 13 min
  • C. 23 min
  • D. 9 min

Explanation: The two taps together fill at 1/10 + 1/15 = 1/6 of the cistern per minute.

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Correct answer: 9 min
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