Time taken by Rahul to complete work alone

CAT 2021 Slot 3 · QA · Easy · Work and time

All CAT 2021 Slot 3 questionsMore Work and time questionsAll CAT QA

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

Explanation

Let Rahul's rate of work be rr per hour and Gautam's rate be gg per hour.

In the first case, Rahul works from 9 AM to 5 PM (8 hours) and Gautam works from 11 AM to 5 PM (6 hours): 8r+6g=18r + 6g = 1 --(1)

In the second case, both work together from 9 AM for 7.5 hours (30 minutes earlier than 5 PM): 7.5(r+g)=1  ⟹  r+g=17.5=2157.5(r + g) = 1 \implies r + g = \frac{1}{7.5} = \frac{2}{15} 6r+6g=1215=456r + 6g = \frac{12}{15} = \frac{4}{5} --(2)

Subtracting (2) from (1): 2r=1−45=15  ⟹  r=1102r = 1 - \frac{4}{5} = \frac{1}{5} \implies r = \frac{1}{10}

So Rahul alone would take 1r=10\frac{1}{r} = 10 hours to complete the work.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace