Two pipes can fill a tank in 10 hours and 12 | vedclass

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Question

(A) Let the rates of the three pipes be $A, B,$ and $C$ respectively.Rate of pipe $A = 1/10$ tank per hour.Rate of pipe $B = 1/12$ tank per hour.Rate

Vedclass · Accepted Answer

$7 	ext{ hours } 30 	ext{ minutes}$

Vedclass · Answer

(A) Let the rates of the three pipes be $A, B,$ and $C$ respectively.Rate of pipe $A = 1/10$ tank per hour.Rate of pipe $B = 1/12$ tank per hour.Rate of pipe $C$ (emptying) $= -1/20$ tank per hour.When all three pipes are open simultaneously,the net rate of filling is:$(1/10 + 1/12 - 1/20) 	ext{ tank per hour}$.Taking the least common multiple $(LCM)$ of $10, 12,$ and $20$,which is $60$:Net rate $= (6/60 + 5/60 - 3/60) = 8/60 = 2/15$ tank per hour.Time taken to fill the tank $= 1 / (2/15) = 15/2 = 7.5$ hours.$7.5$ hours is equal to $7$ hours and $30$ minutes.

Two pipes can fill a tank in $10$ $hours$ and $12$ $hours,$ while a third pipe can empty the full tank in $20$ $hours.$ If all three pipes operate simultaneously,in how much time will the tank be filled?

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