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(D) A passenger train takes 2 hours more than an express trainto travel a distance of 120 km fronA to station Y. The speed of the passenger train is les than that of the express train by 10 km/hethe average speed of each train.5.(A) SelPo |
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Answer» Answer: speed of the passenger train is 40km/h Speed of the express train is 60km/h Step-by-step explanation: Let the speed of the passenger train is x km/h Speed of the express train is y km/h A/c to question, Passenger train takes 2 hours more than an express train to travel a distance of 240km. Also the speed of the express train is more than that of the passenger train by 20km/h e.g., x + 20 = y .............(1) 240/x = 240/y + 2 .........(2) [ time = distance/speed ] ⇒ 240/x - 240/(x +20) = 2 [ putting equation (1) in equation (2); ] ⇒ 240 [ (x + 20 - x)/x(x +20) ] = 2 ⇒ 120 [ 20/(x² + 20x) ] = 1 ⇒ 120 × 20 = x² + 20x ⇒ x² + 20x - 2400 = 0 ⇒ x² + 60x - 40x -2400 = 0 ⇒ x(x + 60) -40(x + 60) = 0 ⇒ (x + 60)(x - 40) = 0 ⇒ x = 40 and -60 but speed can’t be negative so, x ≠ -60 km/h Hence, speed of the passenger train is 40km/h And speed of the express train is 60km/h |
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