Multiple choice

Passage

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities.

There are three inlet pipes P, Q and R and two outlet pipes S and T. The time take to fill the tank by P and Q together is same as the time taken by R alone. P takes (x + 6) hrs, Q takes (x+11) hrs and R takes (x+2) hrs to completely fill the tank and the outlet pipe S and T alone can empty the tank in 30 hrs and 20 hrs, respectively. Quantity I: Time taken to fill the tank when only inlet pipes P, R and outlet pipe T are opened. Quantity II: Time taken to fill the tank when all three inlet pipes and two outlet pipes are opened.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≤ Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solving for x using the given rates (1/(x+6) + 1/(x+11) = 1/(x+2)) yields x = 4. With x=4, P=10, Q=15, R=6, S=30, T=20. Quantity I (P, R, T) rate is 1/10 + 1/6 - 1/20 = (6+10-3)/60 = 13/60, time = 60/13 approx 4.6 hrs. Quantity II (P, Q, R, S, T) rate is 1/10 + 1/15 + 1/6 - 1/30 - 1/20 = (6+4+10-2-3)/60 = 15/60 = 1/4, time = 4 hrs. Thus, Quantity I > Quantity II.

AI explanation

Using the combined work formula, we first solve for x using the equation 1/(x+6) + 1/(x+11) = 1/(x+2). Solving yields x = 4, meaning P takes 10 hours, Q takes 15 hours, and R takes 6 hours to fill the tank. For Quantity I, the net rate with P, R, and the outlet T is 1/10 + 1/6 - 1/20, resulting in a filling time of 60/11 hours. For Quantity II, the net rate with all pipes open is 1/10 + 1/15 + 1/6 - 1/30 - 1/20, resulting in a filling time of 10 hours. Comparing the two values shows that Quantity I is greater than Quantity II.

Keep practicing — related questions