Question
Quantity-I: Pipe P fills an
empty tank in 25 hours, while pipe Q fills it in 40 hours. If the tank is initially 36% full, pipe P operates for 6 hours before being shut off. Determine how much time pipe Q will take to fill the rest of the tank. Quantity-II: Determine the time a bus will take to cover a distance of 1080 km, given its constant speed is 20 m/s. In the question, two Quantities I and II are given. You have to solve both the Quantity to establish the correct relation between Quantity-I and Quantity-II and choose the correct option.Solution
ATQ, Quantity I: Let total capacity of the tank = 200 litres (LCM of 25 and 40) Efficiency of pipe ‘P’ = 200/25 = 8 litres/hour Efficiency of pipe ‘Q’ = 200/40 = 5 litres per hour Quantity of water to be filled = 0.64 × 200 = 128 litres Quantity of water filled by tap ‘P’ in 6 hours = 6 × 8 = 48 litres Desired time = (128 – 48)/5 = 80/5 = 16 hours So, Quantity I = 16 hours Quantity II: Speed of bus = 20 × 18/5 = 72 km/h Desired time = 1080/72 = 15 hours So, Quantity II = 15 hours Therefore, Quantity I > Quantity II
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