Three pipes A, B & C fill a tank in 3 hours working simultaneously. The pipe C is twice as faster as B and B is twice as fast as A. The time taken by pipe A alone to fill the tank is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 21 hours
Let pipe A alone fill the tank in T hours, so it fills \(\frac{1}{T}\) of the tank per hour. B is twice as fast and C twice as fast as B, so the rates of filling are
\( \displaystyle A: \frac{1}{T}, \quad B: \frac{2}{T}, \quad C: \frac{4}{T} \)
Together they fill \(\frac{1}{3}\) of the tank per hour:
\( \displaystyle \frac{1}{T} + \frac{2}{T} + \frac{4}{T} = \frac{1}{3} \)
\( \displaystyle \frac{7}{T} = \frac{1}{3} \)
\(T = 21\)
So pipe A alone takes 21 hours.