a) at 10 o’clock & 5:30 o’clock

b) at 7 o’clock & 12:30 o’clock

c) at 6 o’clock & 10:30 o’clock

d) at 12 o’clock & 7:30 o’clock

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.