Multiple choice

Find the correct relationship between given quantities. Quantity I: Number of days to finish the work, if A can do a work in 40 days, B can do in 48 days, and C can do in 80 days. A work with B on first day and with C on next day, this sequence is follow till the end of whole work. Quantity II: Number of days to finish the work, If A and B together can do the work in 27 days, B and C can do in 36 days and C and A can do in 54 days. Then A, B and C together finish the work.

  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
E Correct answer
Explanation

Quantity I: A works with B on day 1, then with C on day 2, alternating. A+B = 1/40+1/48 = 11/240 per day. A+C = 1/40+1/80 = 3/240 per day. In 2 days, work done = 14/240. Extending this pattern, total time is approximately 35.2 days. Quantity II: From pair rates, we get A=1/72, B=1/108, C=1/216. Combined A+B+C = 6/216 = 1/36, so 36 days. Since 35.2 ≈ 36, the relationship is 'cannot be established' as they're approximately equal but not exactly.

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