Two taps would fill a cistern in 18 and

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