Correct answer is : d) 14 hours 30 minutes

Explanation

We know, time = \frac{distance}{speed}
In 1st case,
The man goes 3 km uphill at 1 km/hour.
\therefore Time taken to go uphill is = \frac{3}{1} hours
= 3 hours.
The man goes 8 km on level ground at 4 km/hour.
\therefore Time taken on level ground is = \frac{8}{4} hours
= 2 hours
The man goes 6 km downhill at 6 km/hour.
\therefore Time taken to go downhill is = \frac{6}{6} hours
= 1 hours
\therefore\ Total time to go P to Q is = \left(3+2+1\right) hours
= 6 hours

In 2nd case,
When returning from Q to P then the uphill distance will convert the downhill distance and the downhill distance will convert the uphill distance.
\therefore\ The man returns 6 km uphill at 1 km/hour.
\therefore Time taken to return uphill is = \frac{6}{1} hours
= 6 hours
The man returns 8 km on level ground at 4 km/hour.
\therefore Time taken on level ground is = \frac{8}{4} hours
= 2 hours.
The man returns 3 km downhill at 6 km/hour.
\therefore Time taken to return downhill is = \frac{3}{6} hours
= \frac{1}{2} hours
\therefore\ Total time to returns Q to P is = \left(6+2+\ \frac{1}{2}\ \right) hours
= 8 hours 30 minutes

\therefore The total time go and return from P to Q and Q to P,
The man will take = \left(6\ hours\ +\ 8\ hours\ 30\ minutes\right)
= 14 hours 30 minutes.
Ans: Total time is 14 hours 30 minutes.