There is a water-cask with three different water-taps. With the smallest tap the water-cask can be filled in 20 minutes. With middle the tap the water-cask can be filled in 12 minutes. With the largest tap the water-cask can be filled in 5 minutes. The Question: How long does it take to fill the water-cask with the three taps together?

general knowledge math & puzzles

  1. 3.5 min

  2. 2.5 min

  3. 4 min

  4. 3 min

Show answer
Correct Option: D

AI Explanation

To find the time it takes to fill the water-cask with all three taps together, we need to calculate the combined rate at which the taps fill the cask.

Let's denote the rates of the smallest, middle, and largest taps as R1, R2, and R3 respectively. The time it takes to fill the cask with each tap can be expressed as follows:

Time with smallest tap = 20 minutes (1/R1) Time with middle tap = 12 minutes (1/R2) Time with largest tap = 5 minutes (1/R3)

To find the combined rate, we can add the rates of the individual taps:

Combined rate = R1 + R2 + R3

Now, let's find the rates of the taps:

Rate with smallest tap (R1) = 1/20 cask per minute Rate with middle tap (R2) = 1/12 cask per minute Rate with largest tap (R3) = 1/5 cask per minute

To find the combined rate, we add the rates:

Combined rate = (1/20) + (1/12) + (1/5) = (3/60) + (5/60) + (12/60) = 20/60 = 1/3 cask per minute

The combined rate is 1/3 cask per minute, which means it takes 3 minutes to fill the water-cask with all three taps together.

Therefore, the correct answer is D) 3 min.

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