A tank has two pipes. The first pipe can fill | vedclass

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(D) Let the total capacity of the tank be $180$ units ($LCM$ of $45$ and $60$).Efficiency of the first pipe (filling) $= 180 / 45 = +4$ units/min.Effi

Vedclass · Accepted Answer

$5 	ext{ hrs } 53 	ext{ min}$

Vedclass · Answer

(D) Let the total capacity of the tank be $180$ units ($LCM$ of $45$ and $60$).Efficiency of the first pipe (filling) $= 180 / 45 = +4$ units/min.Efficiency of the second pipe (emptying) $= 180 / 60 = -3$ units/min.In a cycle of $2$ minutes (first pipe on for $1$ min,second pipe on for $1$ min),the net work done $= 4 - 3 = 1$ unit.To avoid overflowing,we consider the capacity before the last filling step: $180 - 4 = 176$ units.It takes $176$ cycles to fill $176$ units,which equals $176 	imes 2 = 352$ minutes.In the next minute ($353^{	ext{rd}}$ minute),the first pipe fills the remaining $4$ units.Total time $= 352 + 1 = 353$ minutes $= 5$ hours and $53$ minutes.

$A$ tank has two pipes. The first pipe can fill it in $45$ minutes and the second can empty it in $1$ hour. In what time will the empty tank be filled if the pipes are opened one at a time in alternate minutes?

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