Multiple choice

Two pipes A and B together can fill a tank in 20 hours. Ratio of efficiency A and B is 5 : 4. They together filled the tank for the first 4 hours. Then B is closed and another pipe C is opened. Now if tank is filled in another 9 hours then Pipe C alone can fill the tank in how many hours.

  1. 90/7 hour

  2. 80/5 hour

  3. 180/11 hour

  4. 180/7 hour

  5. 90/11 hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Efficiency ratio A:B = 5:4. Let A=5k, B=4k. Together they fill 1/20 of the tank per hour. 9k = 1/20, so k = 1/180. A=5/180, B=4/180. In 4 hours, they fill 4 * (9/180) = 36/180 = 1/5. Remaining tank = 4/5. Pipe B is closed, C is opened. A+C fill 4/5 in 9 hours, so A+C = (4/5)/9 = 4/45. Since A=1/36, C = 4/45 - 1/36 = (16-5)/180 = 11/180. C fills the tank in 180/11 hours.

AI explanation

Using the given efficiency ratio of 5:4, pipe A fills the tank in 20 * (9/5) = 36 hours and pipe B in 20 * (9/4) = 45 hours. In the first 4 hours, A and B fill 4 * (1/36 + 1/45) = 1/5 of the tank. Pipe A fills 9/36 = 1/4 of the tank during the remaining 9 hours, meaning pipe C must fill 1 - 1/5 - 1/4 = 11/20 of the tank in 9 hours. Pipe C fills 11/180 of the tank per hour, so the time taken by pipe C alone is 180/11 hours. The required time is 180/11 hour.

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