Question

Two pipes running together can fill a cistern in $\frac{12}{17}$ minutes. If one pipe takes 4 minutes more than the other to fill it, write the second degree equation from which we can find time taken by the pipe to fill the cistern.

• A. $17x^2+44x-48=0$
• B. $17x^2+44x-38=0$
• C. $17x^2+54x-48=0$
• D. $17x^2+24x-48=0$

Answer 1

The correct option is A

$17x^2+44x-48=0$

Suppose the first pipe takes $x$ minutes to fill the cistern. Then the second pipe will take $(x+4)$ minutes to fill the cistern.

$\therefore$ Portion of the cistern filled by the first pipe in one minute $=\frac{1}{x}$

$\Rightarrow$ Portion of the cistern filled by the second pipe in one minute $=\frac{1}{x+4}$

It is given that the cistern is filled in $\frac{12}{17}$ minutes.

$\Rightarrow$ Portion of the cistern filled in one minute by both pipes together $=\frac{17}{12}$

$\Rightarrow \frac{1}{x}+\frac{1}{x+4}=\frac{17}{12}$

$\frac{x+4+x}{x(x+4)}=\frac{17}{12}$

$\Rightarrow 12(2x+4)=17x(x+4)$

$\Rightarrow 24x+48=17x^2+68x$

$\Rightarrow 17x^2+44x-48=0$