Quantity I: The time taken by a bike to cross a tunnel and a bridge is 36 seconds and 30 seconds, respectively. If the length of the tunnel exceeds the length of the bridge by 96 meters, how much time (in minutes) will the bike take to cover a distance of 4.32 km? Quantity II: A and B can together complete a task in 5 hours, and A's efficiency is twice that of
B. If A works at 5/3 of his normal efficiency, how long (in hours) will it take A to finish the task alone?

Answer: E Quantity I: Let the length of bridge = ‘d’ m So, the length of tunnel = (d + 96) m Also let the speed of bike = ‘x’ m/s So,                         d/x = 30 d = 30x -----------(1) And, (d + 96)/x= 36 From equation (1): 30x + 96 = 36x x = 16 m/s So, time taken by bike to cover 4.32 km = (4.32 * 1000)/16 = 270 seconds = 4.5 minutes Quantity II: Let time taken by A alone to finish the work = ‘t’ hours So, time taken by B alone to finish the work = ‘2t’ hours (1/t) + (1/2t) = 1/5 3/2t = 1/5 t = 7.5 Time taken by A alone finish the work with its original efficiency = 7.5 hours So, time taken by A alone to finish the work with 5/3 of its original efficiency = 7.5 * (3/5) = 4.5 hours Hence, Quantity I = Quantity II