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Two trains are 100 km apart are traveling in the same direction if the speed of the faster train is 50 km/hr and the slower train is x km/hr and the faster train takes x/6 hours to overtake the slower train, then what can be the speed of the slower train?1. 40 km/hr or 20 km/hr2. 30 km/hr or 20 km/hr3. 30 km/hr4. 30 km/hr or 50 km/hr |
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Answer» Correct Answer - Option 2 : 30 km/hr or 20 km/hr Given: Distance between trains = 100 km Speed of faster = 50 km/hr Speed of slower train = x km/hr Time taken to overtake = x/6 hour Concept used: When A and B travel in the same direction = Relative speed becomes A – B (i.e. Relative speed is difference of their individual speed when they travel in same direction) When A and B travel towards each other = Relative speed becomes A + B (i.e. Relative speed is sum of their individual speed when they travel towards each other) Time = Distance/Speed Calculation: Relative speed = (50 – x) km/hr Time taken = Distance between them/Relative speed ⇒ x/6 = 100/(50 – x) ⇒ x × (50 – x) = 6 × 100 ⇒ 50x – x2 = 600 ⇒ x2 – 50x + 600 = 0 ⇒ x2 – 30x – 20x + 600 = 0 ⇒ x × (x – 30) – 20 × (x – 30) = 0 ⇒ (x - 20) × (x - 30) = 0 ⇒ x = 30 and x = 20 There are two values of x which satisfy the given conditions. ∴ The speed of slower train can be 30 km/hr or 20 km/hr |
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