If two pipes function together, the tank will be filled in 12 h . One pipe fills the tank in 10 h faster than the other. How many hours does the faster pipe take to fill up the tank?

20 h
60 h
15 h
25 h

Correct Answer: 20 h

Explanation:

Let one pipe takes m h to fill the tank.
Then, the other pipe takes (m - 10) h.
According to the question.
∴ 1/m + 1/(m - 10) = 1/12
⇒ (m - 10 + m)/{m(m - 10)} = 1/12
⇒ 12m( m - 10 + m ) = ( m - 10 )
⇒ m² - 34m + 120 = 0
⇒ m² - 30m - 4m + 120 = 0
⇒ ( m - 30 )( m - 4 ) = 0
∴ m = 30 or 4
∴ Faster pipe will take ( 30 - 10 ) h = 20 h to fill the tank.

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