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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

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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.

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