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Work and Time Allocation

CAT 2024 Slot 1 · Quantitative Ability · Easy · Time and Work

This is an easy Quantitative Ability question from the CAT 2024 Slot 1 paper. It tests Time and Work. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is

Answer

6

Explanation

Total work = 15×4=6015 \times 4 = 60 person-hours for Renu = 8×5=408 \times 5 = 40 person-hours for Seema. Let total work = 120120 units.

  • Renu's rate = 120/60=2120 / 60 = 2 units/hour.
  • Seema's rate = 120/40=3120 / 40 = 3 units/hour.

Given:

  • Renu works 2 hours/day.
  • Seema works double the hours of Renu = 4 hours/day.
  • Let Seema work for DD days   ⟹  \implies Renu works for 2D2D days.

Total work done: Renu: 2D×2 hours/day×2 units/hour=8D\text{Renu: } 2D \times 2 \text{ hours/day} \times 2 \text{ units/hour} = 8D Seema: D×4 hours/day×3 units/hour=12D\text{Seema: } D \times 4 \text{ hours/day} \times 3 \text{ units/hour} = 12D 8D+12D=120  ⟹  20D=120  ⟹  D=68D + 12D = 120 \implies 20D = 120 \implies D = 6

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