Two pipes A & B would fill a tank in 20 & 30 minutes respectively. Both pipes being open, find when A must be turned off so that tank may be just filled in 15 minutes.

Two pipes A & B would fill a tank in 20 & 30 minutes respectively. Both pipes being open, find when A must be turned off so that tank may be just filled in 15 minutes. Correct Answer After 10 minutes

Let the time be T minutes after which pipe A need to turned off. Both of the pipes remain open together only for T minutes. Pipe A fills 1/20 of the tank in 1 minute. Pipe B fills 1/30 of the tank in 1 minute Together in 1 minute they fill (1/20 + 1/30 = 1/12) of the tank. Together in T minutes they fill = T/12 of the tank In (15 - T) minutes, pipe B alone can fill = (15 - T)/30 of the tank Now, T/12 +  (15 - T)/30 = 1 or,  {15T + 6(15 - T)}/180 = 1 or, (15T + 90 - 6T) / 180 = 1 or,  9T = 180 - 90 or,  9T = 90 So, T =  10 minutes
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