Question

Two pipes can fill a tank in $15$ hours and $20$ hours respectively, while the third can empty it in $30$ hours. If all the pipes are opened simultaneously, the empty tank will be filled in

• A. $10$ hours
• B. $12$ hours
• C. $15$ hours
• D. $15\frac{1}{2}$ hours

Answer 1

The correct option is B $12$ hours

Let the capacity of the tank be $60$ units (LCM of $15$, $20$ & $30$).
Pipe A fills = $\frac{60}{15}=4$ units / hour
Pipe B fills = $\frac{60}{20}=3$ units / hour
Pipe A fills = $\frac{60}{30}=2$ units / hour
(A + B + C)'s together per hour work = $(4+3-2)=5$ units/hour
Time taken by all three to fill an empty tank = $\frac{60}{5}=12$ hours.