Question
Two taps would fill a cistern in 18 and
24 minutes respectively. Both taps being opened. Find when the Ist tap must be turned off so that the cistern may be just filled in 12 minutes.Solution
First tap fills `1/18` of the cistern in 1 minute Second tap `1/24` fills of the cistern in 1 minute. First tap is turned off and the tank is filled in 12 mts. `1/24xx12 = 1/2` of the tank is filled by the second tap in 12 minutes. `1/2` of the tank is filled by the 1st tap in= `18/1xx1/2 = 9mts.` Alternate Method: I II Time 18 24 LCM 72 units Eff 4 : 3 As 1st pipes is closed so 2nd pipes is for whole time , Hence 2nd pipe will finish = 3 `xx` 12=36 units So remaining = 72 - 36 = 36 units which is done by Ist, Hence 1st tap worked for = 36/4 = 9 minutes
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