Multiple choice

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

  1. $2\ hrs\ 15\ min$
  2. $4\ hrs\ 24\ min$
  3. $5\ hrs$
  4. $3\ hrs$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills 1/4 of the tank per hour, and Pipe B fills 1/5 per hour. In two hours (one hour each), they fill 1/4 + 1/5 = 9/20 of the tank. After 4 hours, they have filled 18/20 = 9/10 of the tank, leaving 1/10 to be filled by Pipe A, which takes 1/10 / (1/4) = 0.4 hours or 24 minutes.

AI explanation

Using the least common multiple, let the total capacity be 20 units, making the rate of pipe A 5 units per hour and pipe B 4 units per hour. Working alternately for two hours, they fill 9 units, so after 4 hours they fill 18 units. The remaining 2 units are filled by pipe A in the fifth hour at a rate of 5 units per hour, which takes 2 divided by 5 of an hour, or 24 minutes; the total time is 4 hours and 24 minutes.

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