Question

Ramesh walks from home at a speed of 20 kmph and reaches the police station 30 min late. Next time he increases his speed by 4 kmph but still reaches late by 10 min. Find the distance of the police station from his home. 
1. 30 km
2. 20 km
3. 40 km
4. 50 km

Answer 1

Correct Answer - Option 3 : 40 km

Given:

Speed (a) = 20 kmph

Time late (t₁) = 30 min

Increased Speed (b) = 4 kmph

Time late (t₂) = 10 min

Formula Used:

Distance = (t1 – t2) × (a + b) a/b

Calculations:

a = 20 kmph , t₁ = 30 min , b = 4 kmph , t₂ = 10 min

According to the formula,

Distance = (t₁ – t₂) × (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.