1. Four taps an individually fill a cistern of water in 1 hour, 2 hours, 3 hours and 6 hours respectively. If all the four taps are opened simultaneously, the cistern can be filled in how many minutes ?A20B30C35D40
Question
- Four taps an individually fill a cistern of water in 1 hour, 2 hours, 3 hours and 6 hours respectively. If all the four taps are opened simultaneously, the cistern can be filled in how many minutes ?A20B30C35D40
Solution
To solve this problem, we first need to understand that the rate of filling the cistern is additive when all taps are opened simultaneously.
- The first tap can fill the cistern in 1 hour, so its rate is 1 cistern/hour.
- The second tap can fill the cistern in 2 hours, so its rate is 1/2 cistern/hour.
- The third tap can fill the cistern in 3 hours, so its rate is 1/3 cistern/hour.
- The fourth tap can fill the cistern in 6 hours, so its rate is 1/6 cistern/hour.
When all taps are opened simultaneously, their rates are added together. So, the combined rate is 1 + 1/2 + 1/3 + 1/6 = 2 cisterns/hour.
Therefore, to fill one cistern, it would take 1/2 hour, or 30 minutes. So, the answer is B30.
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