correct answer is : d) at 12 o’clock & 7:30 o’clock

Explanation

According to the question,
At 3 o’clock Ram has completed \ \frac{2}{5} of his journey.
And, at 5 o’clock Ram has completed \ \frac{2}{3} of his journey.
So, Distance covered at (5 o’clock – 3 o’clock) = 2 hours was :
= \left(\ \frac{2}{3}\ -\frac{2}{5}\ \right)
= \left(\ \frac{10\ -\ 6}{15}\ \right)
= \ \frac{4}{15}
2 hours Ram has covered = \frac{4}{15} distance.
\therefore 1 hours Ram has covered =\ \left(\frac{4}{15}\ \div\ 2\right)\ \ distance.
= \left(\frac{4}{15}\ \times\ \frac{1}{2}\ \right) distance
= \frac{2}{15} distance.
So, \frac{2}{15} is Ram’s speed/hr
We know,
Time = \frac{Distance}{Speed}
\therefore Time taken by Ram covered \frac{2}{5}\ of his journey is = \left(\frac{2}{5}\ \div\frac{2}{15}\right) hours
= \left(\frac{2}{5}\ \times\frac{15}{2}\right) hours
= 3 hours.
\therefore Ram started his journey at (3 o’clock – 3 hours) = 12 o’clock
Other side,
Ram covered \frac{2}{3} of his journey at 5 o’clock.
From starting to arrival –
if the total distance is 1,
Then, the remain distance which ram must covered is \left(1\ -\ \frac{2}{3}\right)
= \left(\ \frac{3\ -\ 2}{3}\ \right)
= \frac{1}{3}
\therefore Time taken by Ram covered \frac{1}{3}\ of his journey is = \left(\frac{1}{3}\ \div\frac{2}{15}\right) hours
= \left(\frac{1}{3}\ \times\frac{15}{2}\right) hours
= 2.5 hours.
\therefore Ram arrived his journey at = (5 o’clock + 2.5 hours)
= 7.5 o’clock.
= 7:30 o’clock
Ans: Ram started his journey at 12 o’clock and, Ram arrived his journey at 7:30 o’clock.