Question
Quantity-I: Â A boat requires 15 hours to travel 480 km
upstream. If the speed of the stream is 80% less than the speed of the boat in still water, calculate the downstream speed of the boat. Quantity-II: Â A train takes 32 seconds to pass a bridge that is 160 meters long, and 19.2 seconds to pass a tree. Determine the speed of the train. In this problem, two quantities, I and II, are provided. You are required to solve both quantities and determine the appropriate relationship between Quantity-I and Quantity-II. Select the correct option based on your findings.Solution
ATQ, Quantity I: Upstream speed of the boat = 480 ÷ 15 = 32 km/h Let the speed of the boat in still water be '5b' km/h So, speed of the stream = 5b × 0.2 = 'b' km/h ATQ; 5b - b = 32 Or, 4b = 32 So, b = 8 So, downstream speed of the boat = 5b + b = 6b = 8 × 6 = 48 km/h So, Quantity I = 48 Quantity II: Let the speed of the train be 'd' m/s Length of the train = d × 19.2 = '19.2d' metres ATQ; {(19.2d + 160)/d} = 32 Or, 19.2d + 160 = 32d Or, 160 = 12.8d So, d = 12.5 So, speed of the train = 12.5 × (18/5) = 45 km/h So, Quantity II = 45 So, Quantity I > Quantity II
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