CAT 2021 Slot 3 QA Q9 Time & Work

Question 9 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is
  1. A
    12
  2. B
    11.5
  3. C
    12.5
  4. D
    10

Answer: (D) 10 Time & Work MCQ

Solution

  1. Let Rahul and Gautam do \(r\) and \(g\) of the work per hour.
  2. Actual: Rahul 8 hours, Gautam 6 hours: \(8r + 6g = 1\). Together from 9 AM finishing at 4:30 PM: \(7.5(r + g) = 1\), so \(r + g = \frac{2}{15}\).
  3. \(8r + 6\left(\frac{2}{15} - r\right) = 1 \Rightarrow 2r + 0.8 = 1 \Rightarrow r = 0.1\).
  4. Rahul alone takes 10 hours.

Shortcut. Gautam working 1.5 h fewer than the together-case is covered by Rahul's extra 2 h alone... simplest: Rahul's 2 solo hours equal \(0.5\) h of both, i.e. \(2r = 0.5(r+g)\).

Same concept in other years

See every question on Work completed in phases as workers join, leave or slow down.

More Time & Work questions from CAT

All 34 Time & Work questions asked since 2017.