Two taps A and B can fill an oil tank in 15 m | vedclass

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Question

(A) Let the capacity of the tank be the $LCM$ of $15$ and $18$,which is $90$ units.Efficiency of tap $A = 90 / 15 = 6$ units/min.Efficiency of tap $B

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(A) Let the capacity of the tank be the $LCM$ of $15$ and $18$,which is $90$ units.Efficiency of tap $A = 90 / 15 = 6$ units/min.Efficiency of tap $B = 90 / 18 = 5$ units/min.Combined efficiency of $A$ and $B = 6 + 5 = 11$ units/min.In $6$ min,taps $A$ and $B$ fill $11 	imes 6 = 66$ units.Let the efficiency of the third tap (emptying) be $E$ units/min.After the third tap is opened,the net rate of filling/emptying is $(11 - E)$ units/min.The tank is emptied in $16.5$ min after the third tap is opened,meaning the $66$ units already filled are emptied at a rate of $(E - 11)$ units/min.$66 = (E - 11) 	imes 16.5$$E - 11 = 66 / 16.5 = 4$$E = 15$ units/min.Time taken by the third tap to empty the full tank $= 90 / 15 = 6$ min.

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