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Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.Quantity I: A goods train can cross a station master standing on a platform in 42 seconds whereas it can cross the platform in 18 seconds less than two minutes. Find the length of the platform if the train is 420m long.Quantity II: In 30 seconds a train crosses a tree at a speed of 30 m/s. If it crosses the guard of another train moving in the same direction in 20 s more than a minute, find the length of the second train.1. Quantity I < Quantity II2. Quantity I > Quantity II3. Quantity I ≥ Quantity II4. Quantity I ≤ Quantity II5. Quantity I = Quantity II or relation cannot be established. |
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Answer» Correct Answer - Option 1 : Quantity I < Quantity II Given: Quantity I: Time train takes to cross the station master = 42 s Time train takes to cross the platform = 120 – 18 = 102 s Length of train = 420 m Length of the platform = L Quantity II: Time taken by train to cross a tree = 30 s The speed at which train cross the tree, S1 = 30 m/s Time taken by train to cross the guard of second train = 80 s Concept used: Speed = distance/time Speed by which train crosses the station master = speed of the train Length of the first train, L1 = time taken by it to cross the tree × speed at which it crosses the tree. As the train crosses the guard of second train, time taken = (sum of length of two trains)/speed of first train Calculation: Quantity I: Speed of train, S = length of train/time taken ⇒ S = 420/42 ⇒ S = 10 Time taken by train to cross the platform = distance/speed ⇒ Time = (L + 420)/S ⇒ 102 = (L + 420)/10 ⇒ 102 × 10 = L +420 ⇒ L = 1020 – 420 ⇒ L = 600 m Quantity I = 600 m Quantity II: L1 = 30 × 30 m ⇒ L1 = 900 m Length of second train = L2 Time taken by first train to cross the guard of second train = 80 s ⇒ 80 = (L1 + L2)/S1 ⇒ 80 = (900 + L2)/20 ⇒ 1600 = 900 + L2 ⇒ L2 = 700 m Quantity II = 700 m
∴ From the table, we can see that , Quantity I < Quantity II. |
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