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Two pipes A and B can fill a cistern in 12 min and 16 min respectively. Both the pipes are opened together for a certain time but due to some obstruction the flow of water was restricted to $$\frac{7}{8}$$ of full flow in pipe A and $$\frac{5}{6}$$ of full in pipe B. This obstruction is removed after some time and tank is now filled in 3 min from that moment. How long was it before the full flow.

Two pipes A and B can fill a cistern in 12 min and 16 min respectively. Both the pipes are opened together for a certain time but due to some obstruction the flow of water was restricted to $$\frac{7}{8}$$ of full flow in pipe A and $$\frac{5}{6}$$ of full in pipe B. This obstruction is removed after some time and tank is now filled in 3 min from that moment. How long was it before the full flow. Correct Answer 4.5 min

Let the obstruction remain for x min. Hence,Part of cistern filled in X min + part of cistern filled in 3 min = full cistern$$\left$$    $$ + $$ $$\left$$   = 1$$\frac{{12{\text{x}}}}{{96}} + \frac{7}{{16}} = 1$$Thus,X = 4.5 min.

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