Multiple choice

In the following questions, two quantities are given as Quantity I and Quantity II. Find the correct relationship among them. Quantity I: Three pipes P, Q and R are attached to a tank. Pipe P alone and Pipe Q alone can fill the tank in 30 hours and 20 hours respectively. If pipe P opened for 10 hours and closed, then pipe Q opened for 5 hours and closed and pipe R alone can fill the remaining tank in 5 hours. How many time pipe R alone take to fill the whole tank? Quantity II: Three pipes A, B and C can fill a tank in 10 hours. After working at it together for 3 hours, C is closed and A and B can fill the remaining part in 14 hours. How much time taken by C to fill the tank alone?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: P fills 1/30 per hour, Q fills 1/20 per hour. P works 10 hours = 10/30 = 1/3 tank. Q works 5 hours = 5/20 = 1/4 tank. Remaining = 1 - 1/3 - 1/4 = 5/12. R fills 5/12 in 5 hours, so R's rate = (5/12)/5 = 1/60. R alone takes 60 hours. Quantity II: (A+B+C) together fill in 10 hours, so rate = 1/10. In 3 hours, they fill 3/10. Remaining 7/10 filled by (A+B) in 14 hours, so (A+B) rate = (7/10)/14 = 1/20. C's rate = 1/10 - 1/20 = 1/20. C alone takes 20 hours. Since 60 > 20, Quantity II > Quantity I.

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