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.