A train increases its normal speed by 12.5% and reaches its destination 20 minutes earlier. What is the actual time taken by the train in the journey?

The correct answer is (b).

Let $x$ be the original time taken by the train. If the train increases its speed by 12.5%, then the new time taken is $\frac{112.5}{100}x = \frac{27}{20}x$. Since the new time is 20 minutes earlier, we have $\frac{27}{20}x = x – 20$. Solving for $x$, we get $x = \boxed{180}$ minutes.

Option (a) is incorrect because it is the time taken by the train if it does not increase its speed. Option (c) is incorrect because it is the time taken by the train if it increases its speed by 25%. Option (d) is incorrect because it is the time taken by the train if it increases its speed by 50%.