Multiple choice

Find the value of both quantities and then state the correct relationship. Quantity I: Number of days in which A can alone do the work given A and B can do a work in 80 days, B and C can do a work in 60 days, C and A can do work in 96 days. Quantity II: Number of days in which A can alone do the work given A and B together can complete a work in 80 days. They work together for 10 days then A left the work. If B did the remaining work in 210 days.

  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
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A Correct answer
Explanation

For Quantity I, using total work = 480 units (LCM of 80, 60, 96), we find A's rate = 1.5 units/day, so A alone takes 320 days. For Quantity II, A+B finish 80 days work in 10 days, B completes remaining 70 days work in 210 days, so B alone takes 280 days, meaning A alone takes 80 days. Since 320 > 80, Quantity I is greater.

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