Question

Two taps X and Y can fill a cistern in 32 and 40 minutes respectively. Both the taps are opened into the empty cisterns and after some time tap X is closed. Tap Y alone fills the remaining portion of the cistern. If it took 25 minutes to fill the tank, for how much time(min) was tap X kept open?​

Answer 1

Answer:

• X take to Fill = 32
• Y take to Fill = 40
• Let X isn't open for n minutes

• According to the Question :

$:\Longrightarrow\sf \dfrac{25}{Y} + \dfrac{25 - n}{X} = Total\\\\\\:\Longrightarrow\sf \dfrac{25}{40} + \dfrac{25 - n}{32} = 1\\\\\\:\Longrightarrow\sf \dfrac{5}{8} + \dfrac{25 - n}{32} = 1\\\\\\:\Longrightarrow\sf \dfrac{25 - n}{32} = 1 - \dfrac{5}{8}\\\\\\:\Longrightarrow\sf \dfrac{25 - n}{32} = \dfrac{3}{8}\\\\\\:\Longrightarrow\sf \dfrac{25 - n}{4} =3\\\\\\:\Longrightarrow\sf 25 - n = 12\\\\\\:\Longrightarrow\sf 25 - 12 = n\\\\\\:\Longrightarrow\sf n = 13\: minutes$

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So Tap X was open for (25 - 13) = 12 minutes