Correct Answer - Option 3 : 40 km

**Given:**

Speed (a) = 20 kmph

Time late (t_{1}) = 30 min

Increased Speed (b) = 4 kmph

Time late (t_{2}) = 10 min

**Formula Used:**

Distance = (t1 – t2) × (a + b) a/b

**Calculations:**

a = 20 kmph , t_{1} = 30 min , b = 4 kmph , t_{2} = 10 min

According to the formula,

Distance = (t_{1} – t_{2}) × (a + b) × a/b

⇒ Distance = (30 - 10) / 60 × (20 + 4) × 20/4

⇒ Distance = 20/60 × 24 × 5

⇒ Distance = 8 × 5

⇒ Distance = 40

**The distance of the police station from his home is 40 km.**

**Alternate method:**

Let the distance = x

Here, the difference in time = 30 – 10 = 20 min = 20/60 = 1/3 hr

Speed during next journey = (20 + 4) = 24 kmph

According to the question,

⇒ x/20 – x/24 = 1/3

⇒ (6x – 5x) / 120 = 1/3

⇒ x = 40

**The distance of the police station from his home is 40 km.**