Question

Pipe $A$ can fill a tank in $20$ hours while Pipe $B$ can fill it in $30$ hours and Pipe $C$ can empty the same tank in $40$ hours. If all the pipes are opened together, what will be the time needed to fill the tank completely?

• A. $15\frac{1}{2}$ hours
• B. $18\frac{1}{3}$ hours
• C. $16$ hours
• D. $17\frac{1}{7}$ hours

Answer 1

Answer: (D)

Time taken by pipe A to fill the tank $=20$ hours

Portion of tank filled by pipe A in $1$ hour $=\frac{1}{20}$

Time taken by pipe B to fill the tank $=30$ hours

Portion of Tank filled by pipe B in $1$ hour $\frac{1}{30}$

Time taken by pipe C to empty the tank $=40$ hours

Portion of tank emptied by pipe C in $1$ hour $\frac{1}{40}$

Now, Portion of tank filled by all three pipes together in $1$ hour $=\frac{1}{20}+\frac{1}{30}-\frac{1}{40}$

$=\frac{6+4-3}{120}$

$=\frac{7}{120}$

So, Time taken to filled the tank when all three pipes are opened together

$=\frac{120}{7}=17\frac{1}{7}$ hours