Three fill pipes A, B and C fill a tank in 4, 6 and 8 minutes respectively. Pipe A is opened and after a minute, Pipe B is also opened. Another minute later, Pipe C is also opened. When will the tank be full?

A) \( \Large 2\frac{8}{13} \)
B) \( \Large 1\frac{11}{13} \)

C) \( \Large 3\frac{2}{13} \)
D) \( \Large 1\frac{8}{13} \)

Correct answer:
A) \( \Large 2\frac{8}{13} \)

Description for Correct answer:
In 1 minute, pipe A can fill \( \Large \frac{1}{4} \)th of the tank

In 1 minute, pipe A and B can fill \( \Large \frac{1}{4}+\frac{1}{6}=\frac{5}{12} \)th of the tank

So, in the first two minutes \( \Large \frac{1}{4}+\frac{5}{12}=\frac{2}{3} \)rd of the tank gets filled.

In 1 minute, pipe A, B and C can fill \( \Large \frac{13}{24} \)th of the tank.

Therefore, remaining \( \Large \frac{1}{3} \)rd of the tank can be filled in

\( \Large \frac{1}{3} \times \frac{24}{13}=\frac{8}{13} \) minutes

Totally, in \( \Large 2 + \frac{8}{13} \) minutes the tank will be filled.


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