Question

Two pipes can fill a tank in 12 minutes and 20 minutes respectively. Both
pipes are opened together and after some time the first pipe is closed
and the tank is full in totally 10 minutes. For how many minutes was first
pipe open?

a. 8 Min
b. 6 Min
c. 7 Min
d. 10 Min​

Answer 1

Answer:

Let two pipes A and B can fill a tank completely in 12 minutes and 20 minutes respectively.

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Let pipe A was opened for x minutes.

Pipe B was opened all throughout the filling of tank, hence it was opened for 10 minutes.

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf \dfrac{Time}{A}+\dfrac{Time}{B}=Total\:Work\\\\\\:\implies\sf \dfrac{x}{12}+\dfrac{10}{20} = 1\\\\\\:\implies\sf \dfrac{x}{12}+\dfrac{1}{2} = 1\\\\\\:\implies\sf \dfrac{x}{12} = 1 - \dfrac{1}{2}\\\\\\:\implies\sf \dfrac{x}{12} = \dfrac{1}{2}\\\\\\:\implies\sf x = \dfrac{12}{2}\\\\\\:\implies\sf x = 6 \:minutes$

⠀

$\therefore\:\underline{\textsf{First pipe was op.en for b) \textbf{6 minutes}}}.$