Correct answer is : a) 3 hours 45 minutes

Explanation

Let, the normal speed be ‘x’
And the time taken in normal speed is ‘t’ minutes.
We know,
Distance = speed \times\ time
\therefore In normal speed destination distance is = \left(x\ \times\ t\right)

According to the question,
\frac{3}{5} of x the train taken time is
= \left(t\ +\ 150\right) _{[2 hours 30 minutes = 150 minutes]}
Here, destination distance is
= \left(\frac{3}{5}\ \times\ x\right)\ \times\ \left(t\ +\ 150\right) _{[destination = speed × time]}

As the destination distance is same, so we can compare both distance.
\therefore \left(x\ \times\ t\right) = \left(\frac{3}{5}\ \times\ x\right) \times \left(t\ +\ 150\right)
\rightarrow\ xt\ =\ \ \frac{3x}{5}\ \times\ \left(t\ +\ 150\right)
\rightarrow\ xt\ =\ \ \frac{3xt\ +\ 450x}{5}
\rightarrow\ 5xt\ =\ 3xt\ +\ 450x _{[cross multiplication]}
\rightarrow\ 5xt\ -\ 3xt\ =\ 450x
\rightarrow\ 2xt\ =\ 450x
\rightarrow\ t\ =\ \frac{450x}{2x}
\rightarrow\ t\ =\ 225
\therefore The time taken in normal speed is 225 minutes or 3 hours 45 minutes.
Ans: The time taken in normal speed is 225 minutes or 3 hours 45 minutes.