Multiple choice

Find the correct relationship between given quantities. Two persons, P and Q together can complete a piece of work in 70 days. The efficiency of P is 40% more than that of Q. Quantity I : If P works at 25% of his efficiency then how many days will he take to complete 1/8 of the work? Quantity II : If Q works at 20% of his efficiency then how many days will he take to complete 10% of the work?

  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 relation can't be established

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Q's efficiency = 1 unit/day. P's efficiency = 1.4 units/day (40% more). Together: 2.4 units/day = 1/70 work, so total work = 70 × 2.4 = 168 units. P alone: 168/1.4 = 120 days. Q alone: 168/1 = 168 days. Quantity I: P at 25% efficiency = 0.35 units/day. For 1/8 work = 21 units, time = 21/0.35 = 60 days. Quantity II: Q at 20% efficiency = 0.2 units/day. For 10% work = 16.8 units, time = 16.8/0.2 = 84 days. Since 60 < 84, Quantity I < Quantity II. Key is computing total work first, then adjusting efficiency.