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 (P empties, Q fills): P rate = -1/25 tank/hr Q rate = +1/40 tank/hr Initial filled = 0.36 Water emptied by P in 6 hr = 6*(1/25) = 6/25 = 0.24 Water left after 6 hr = 0.36 - 0.24 = 0.12 Remaining to fill = 1 - 0.12 = 0.88 Time for Q = 0.88 / (1/40) = 0.88*40 = 35.2 hr Quantity I = 35.2 hr Quantity II: Speed = 20 m/s = 72 km/hr Time = 1080/72 = 15 hr Quantity II = 15 hr Comparison: Quantity I > Quantity II
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