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:

Answer: Option D

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,

$$\begin{array}{rl}& 30\times \frac{1}{\text{x}}+40\left(\frac{1}{36}-\frac{1}{\text{x}}\right)=1\\ & \Rightarrow \frac{30}{\text{x}}+\frac{40}{36}-\frac{40}{\text{x}}=1\\ & \Rightarrow \frac{30}{\text{x}}+\frac{10}{9}-\frac{40}{\text{x}}=1\\ & \Rightarrow \frac{10}{\text{x}}=\frac{1}{9}\end{array}$$
Hence, x = 90 minutes.

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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.)