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1. A tank can be filled with water by two pipes A and B together in 36 minutes. If the pipe B was stopped after 30 minutes, the tank is filled in 40 minutes. The pipe B can alone fill the tank in:

A. 45 minutes

B. 60 minutes

C. 75 minutes

D. 90 minutes

Solution:

Let the pipes fill the tank in x minutes.
Part of tank filled by pipes A and B in one minute:

\frac{1}{36}

Part of the tank filled by pipe A in 1 minute =

\frac{1}{36} - \frac{1}{x}

According to the question,

\begin{aligned} 30 \times \frac{1}{x} + 40 (\frac{1}{36} - \frac{1}{x}) = 1 \\ \Rightarrow \frac{30}{x} + \frac{40}{36} - \frac{40}{x} = 1 \\ \Rightarrow \frac{30}{x} + \frac{10}{9} - \frac{40}{x} = 1 \\ \Rightarrow \frac{10}{x} = \frac{1}{9} \end{aligned}

Hence, x = 90 minutes.

Alternatively,
% of tank filled by (A+B) in 1 minute =

\frac{100}{36}

= 2.78%
% of tank filled in 30 minutes = 2.78 × 30 = 83%
That means 17% of tank can be filled by A in last 10 minutes
Then, % tank filled by A in 1 minute =

\frac{17}{10}

= 1.7%
% of tank filled by B in 1 minute = 2.78 - 1.7 = 1.1%
So, B alone can fill 100% tank in,
=

\frac{100}{1.1}

= 90 minutes (approx.)

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