Multiple choice

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values. Quantity I: Time taken to fill the tank when A, B and C are opened in every alternate minute starting with A and ending with C. A, B and C alone takes 20 minutes, 15 minutes and 12 minutes respectively to fill the tank. Quantity II: Find the time taken by waste pipe to empty the full cistern. Two pipes alone can fill a cistern in 10 minutes and 15 minutes respectively. When these two pipes along with the waste pipe are opened, the cistern gets filled in 18 minutes.

  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

Quantity I: A (20 min), B (15 min), C (12 min). Alternate A,B,C starting with A, ending with C: pattern A-B-C-A-B-C... Each 3-min cycle fills 1/20 + 1/15 + 1/12 = (3+4+5)/60 = 12/60 = 1/5 tank. After 5 cycles (15 min), tank full. But it says ending with C, so verify: 15 minutes = 5 full cycles, ends with C. Quantity I = 15 minutes. Quantity II: Two pipes fill in 10 and 15 min. With waste pipe W, tank fills in 18 min. Combined rate = 1/10 + 1/15 - 1/W = 1/18. 1/W = 1/10 + 1/15 - 1/18 = (9+6-5)/90 = 10/90 = 1/9. W empties in 9 minutes. Quantity II = 9 minutes. Since 15 > 9, option A is correct.

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