a) 8 hours 30 minutes

b) 10 hours 30 minutes

c) 12 hours 30 minutes

d) 14 hours 30 minutes

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.