Question : Pipes A and B together can fill an empty tank in $6 \frac{2}{3}$ minutes. If A takes 3 minutes more than B to fill the tank, then the time (in minutes) in which A alone would fill one-third part of the tank is:
Option 1: 6
Option 2: 5
Option 3: 5.5
Option 4: 4.5
Correct Answer: 5
Solution :
Given: Pipes A and B together can fill an empty tank in $6 \frac{2}{3}=\frac{20}{3}$ minutes.
A takes 3 minutes more than B to fill the tank.
Let in $x$ minutes, pipe B by itself can empty the entire tank.
So, the complete tank can be emptied in $(x + 3)$ minutes with just Pipe A.
According to the question,
$\frac{1}{x+3}+\frac{1}{x}=\frac{3}{20}$
⇒ $\frac{x+x+3}{x^2+3x}=\frac{3}{20}$
⇒ $\frac{2x+3}{x^2+3x}=\frac{3}{20}$
⇒ $40x+60=3x^2+9x$
⇒ $3x^2-31x-60=0$
⇒ $3x^2-36x+5x-60=0$
⇒ $3x(x-12)+5(x-12)=0$
⇒ $(x-12)(3x+5)=0$
⇒ $x-12=0$ [since time can not be negative]
⇒ $x=12$
Pipe B takes 12 minutes to empty the entire tank.
The amount of time pipe A needs to empty a full tank is (12 + 3) = 15 minutes
The time in which A alone would fill one-third part of the tank $=15\times \frac{1}{3}=5$ minutes
Hence, the correct answer is 5.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
