A pipe P1 can fill a tank four times as fast as another pipe P2. If together the two pipes can fill the tank in 42 minutes, then the time taken by pipe P2 alone to fill the tank is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 210 minutes
Suppose \( \mathrm{P}_2 \) alone takes \( t \) minutes. Then \( \mathrm{P}_1 \), being four times as fast, takes \( \frac{t}{4} \) minutes.
Their rates of filling are \( \frac{1}{t} \) and \( \frac{4}{t} \) of the tank per minute, and together they fill \( \frac{1}{42} \) of it per minute:
\( \displaystyle \frac{1}{t}+\frac{4}{t}=\frac{1}{42} \)
\( \displaystyle \frac{5}{t}=\frac{1}{42} \)
\( t=5\times 42=210 \)
So \( \mathrm{P}_2 \) alone takes 210 minutes.