Multiple choice

A cistern can be filled by a tap in $4$ hours while it can be emptied by another tap in $9$ hours. If both the taps are opened simultaneously then after how much time will the cistern get filled ?

  1. $4.5$ hrs
  2. $5$ hrs
  3. $6.5$ hrs
  4. $7.2$ hrs
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The net rate of filling is 1/4 - 1/9 = 5/36 tanks per hour. The time to fill the cistern is 36/5 = 7.2 hours.

AI explanation

Using the net work formula, the fill tap completes 1/4 of the cistern per hour and the empty tap removes 1/9 per hour. Their combined rate is 1/4 - 1/9 = 9/36 - 4/36 = 5/36 per hour. The time to fill the cistern is the reciprocal of this rate, which is 36/5 = 7.2 hours.

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