Pipe $A$ can fill an empty tank in $5$ hours while Pipe $B$ can empty the full tank in $6$ hours. If both are opened in the empty tank, time taken to fill it up completely is __________.

30 h o u r s

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20 h o u r s

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10 h o u r s

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40 h o u r s

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Solution

The correct option is A $30 h o u r s$
Let total size of tank be 1 unit
A's one hour water contribution $= 1 / 5$ units
B's one hour water contribution $= - 1 / 6$ units ( minus sign for emptyting tank)
(A+B)'s one hour water output= $1 / 5 - 1 / 6 = 1 / 30$
Time needed by (A+B) to fill whole tank= $\frac{1}{1 / 30}$ hours= $30$ hours

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Pipe A can fill an empty tank in 5 hours while Pipe B can empty the full tank in 6 hours. If both are opened in the empty tank, time taken to fill it up completely is __________.

The correct option is A 30 hoursLet total size of tank be 1 unitA's one hour water contribution=1/5 unitsB's one hour water contribution=−1/6 units ( minus sign for emptyting tank)(A+B)'s one hour water output= 1/5−1/6=1/30Time needed by (A+B) to fill whole tank= 11/30 hours=30 hours

Pipe $A$ can fill an empty tank in $5$ hours while Pipe $B$ can empty the full tank in $6$ hours. If both are opened in the empty tank, time taken to fill it up completely is __________.