Question

One pipe can fill a cistern in $3hours$ less than the other. The two pipes together can fill the cistern in $6hours$ $40minutes$. Find the time that each pipe will take to fill the cistern.

• A. $12hrs$ and $15hrs$
• B. $13hrs$ and $15hrs$
• C. $12hrs$ and $16hrs$
• D. $Noneoftheabove$

Answer 1

The correct option is A $12hrs$ and $15hrs$

Let the pipe can fill the cistern be $x$ and $x-3$ hours.
Two pipes together can fill the cistern in $6$ hours $40$ minutes $=$ $\frac{1}{x}+\frac{1}{x-3}$

Time taken for both the pipes to fill the cistern $=6$ hours $40$ minutes

$=6\frac{40}{60}=6\frac{2}{3}=\frac{20}{3}$

Therefore, part of the tank filled by both pipes together in 1 hour $=$ $\frac{3}{20}$

So,

$\frac{1}{x}+\frac{1}{x-3}=\frac{3}{20}$

$\Rightarrow \frac{x-3+x}{x(x-3)}=\frac{3}{20}$

$\Rightarrow \frac{2x-3}{x^2-3x}=\frac{3}{20}$

$\Rightarrow 40x-60=3x^2-9x$

$\Rightarrow 3x^2-49x+60=0$

$\Rightarrow 3x^2-49x+60=0$

$\Rightarrow \frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\Rightarrow \frac{49\pm \sqrt{(-49{)}^2-4\times 60\times 3}}{2\times 3}$

$\frac{49\pm \sqrt{1681}}{6}\Rightarrow \frac{49\pm 41}{6}$

$\Rightarrow 15$ or 1.33

Cannot take $x=1.33$ because $(x-3)$ will be negative.
Therefore, $x=15$

The pipe can fill the cistern be $15$ hours and $15-3=12$ hours.