Pipes A and B together can fill a tank in 6 hours. The empty tank is also filled completely when pipe A is kept open for 4 hours and pipe B for 9 hours. How long will pipe A alone take to fill the tank?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10 hours
Let pipe A fill \(a\) of the tank in 1 hour and pipe B fill \(b\) of the tank in 1 hour. Each situation gives one equation for the parts filled.
\(\displaystyle a + b = \frac{1}{6}\)
\(4a + 9b = 1\)
Multiplying the first equation by 4 and subtracting it from the second:
\(\displaystyle 5b = 1 - \frac{4}{6} = \frac{1}{3}\)
\(\displaystyle b = \frac{1}{15}\)
\(\displaystyle a = \frac{1}{6} - \frac{1}{15} = \frac{5 - 2}{30} = \frac{1}{10}\)
So pipe A alone fills the tank in 10 hours (and pipe B alone in 15 hours).
Why the other options are incorrect
Option (1) 15 hours — Incorrect. 15 hours is the time of pipe B alone, not of pipe A.
Option (2) 12 hours — Incorrect. B would then fill \(\frac{1}{6} - \frac{1}{12} = \frac{1}{12}\) per hour, and 4 hours of A with 9 hours of B would fill \(\frac{13}{12}\) of the tank, not exactly 1.
Option (3) 9 hours — Incorrect. B would then fill \(\frac{1}{6} - \frac{1}{9} = \frac{1}{18}\) per hour, and 4 hours of A with 9 hours of B would fill only \(\frac{17}{18}\) of the tank.