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$ 12 $ Pipes, all of the same size, fill a tank in $ 42 $ minutes. How long will it take to fill the same tank, if $ 21 $ pipes of the same size are used?

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Last updated date: 14th Jul 2024
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Answer
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Hint: First of all, we shall note some important terms from the given question and they are pipes, tank, and minutes. In the given question, we got information that twelve pipes, all of the same size, fill a tank in $ 42 $ minutes. And our question is to calculate how long it will take to fill the same tank, if $ 21 $ pipes of the same size are used.
Here, we need to calculate how long it will take for $ 1 $ pipe to fill the same tank. If we find the time required for a $ 1 $ pipe, then we can easily find how long it will take to fill the same tank, if $ 21 $ pipes of the same size are used and it is our required solution too.

Complete step by step answer:
Given that twelve pipes can fill a tank in $ 42 $ minutes.
To find: The time required for $ 21 $ pipes to fill the tank.
Before calculating the time required for $ 21 $ pipes to fill the tank, we need to find how long it will take for $ 1 $ pipe to fill the same tank.
The time required for $ 12 $ pipes to fill the tank $ = 42 $ minutes
The time required for $ 1 $ pipe to fill the tank \[ = 42 \times 12\]
Hence, the time required for $ 1 $ pipe to fill the tank \[ = 42 \times 12\]minutes…… $ \left( 1 \right) $
Now, we shall get into our claim.
When we divide the equation $ \left( 1 \right) $ by $ 21 $ on the right side, we will get our required answer.
That is, the time required for $ 21 $ pipes to fill the tank \[ = \dfrac{{42 \times 12}}{{21}}\]
Hence, the time required for $ 21 $ pipes to fill the tank \[ = 24\]minutes
Therefore, $ 21 $ pipes take $ 24 $ minutes to fill the tank.

Note: First we need to calculate how long it will take for a $ 1 $ pipe to fill the same tank. If we find the time required for a $ 1 $ pipe, then we can easily find how long it will take to fill the same tank, if $ 21 $ pipes of the same size are used and it is our required solution too.