Option 3 : 70 km

If the distance is constant, then the time varies inversely with speed.

Let the speed of man to cover A to B be S_{1} and from B to A be S_{2}

And the time taken to cover from A to B be T_{1} and from B to A be T_{2}

According to the question, S_{1} ∶ S_{2} = 1 ∶ 2

So, T_{1} ∶ T_{2} = 2 ∶ 1

Again, according to the question

Total time taken by the man = 5h 15 min

⇒ R + 2R = (5 + 15/60) h

⇒ 3R = (5 + 1/4)

⇒ 3R = 21/4

⇒ R = 7/4 h

So, time taken to cover A to B = 2R

⇒ 2 × 7/4

⇒ 7/2 h

The distance between A and B = S_{1} × T_{1}

⇒ 20 × 7/2

⇒ 10 × 7

⇒ 70 km

∴ The distance between A and B is 70 km.

Given,

A man goes from point A to B with a speed of 20 km/hr

The man comes from point B to A with a speed of 40 km/hr

Total time to cover whole journey = 5 hrs 15 minutes.

Formula:

Speed = distance/time

1 hr = 60 min

Calculation:

3 hrs 15 min = (5 + 15/60) hr = (5 + 1/4) = 21/4 hr

Let distance between A and B be x km, then

According to the question,

x/20 + x/40 = 21/4

⇒ (2x + x)/40 = 21/4

⇒ 3x/40 = 21/4

⇒ x = 7/4 × 40

⇒ x = 7 × 10

⇒ x = 70

**∴ **The distance** between A and B is 70 km.**

If the distance is constant, then the time varies inversely with the speed.