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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 km2. 20 km3. 40 km4. 50 km |
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Answer» 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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