Two pipes A and B running together can fill a tank in 6 minutes. If pipe A takes 5 minutes less than pipe B to fill the tank, then the time taken by pipe A to fill the tank alone is,
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10 minutes
Let pipe A alone take t minutes; then pipe B takes t + 5 minutes. In one minute the two pipes together fill \( \frac{1}{6} \) of the tank:
\( \displaystyle \frac{1}{t}+\frac{1}{t+5}=\frac{1}{6} \)
\( \displaystyle 6(t+5)+6t=t(t+5) \)
\( \displaystyle t^2-7t-30=0 \)
\( \displaystyle (t-10)(t+3)=0 \)
\( \displaystyle t=10\ \text{(time cannot be negative)} \)
So pipe A alone fills the tank in 10 minutes (and pipe B in 15 minutes).
Check: \( \frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}=\frac{1}{6} \).