CAT 2021 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 9

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 9 : 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. 12
  2. 11.5
  3. 12.5
  4. 10

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Explanatory Answer

Let R be the fraction of work done by Rahul in 1 hour.
and G be the fraction of work done by Gautam in 1 hour.
Initially Rahul works from 9AM to 5PM (8 hours) and Gautam works for 2 hours less.
8R + 6G = 1 whole unit of work
If they start together they finish 30 minutes earlier or if they start at 9 AM, they finish at 4:30PM (7.5 hours)
7.5R + 7.5G = 1 whole unit of work
8R + 6G = 7.5R + 7.5G
0.5R = 1.5G
R = 3G
This means Rahul is thrice as efficient as Gautam.
8R + 6G = 1 whole unit of work
8R + 2R = 1 whole unit of work
10R = 1 whole unit of work
R is the fraction of work done by Rahul in 1 hour.
Since 10R = 1
R alone takes 10 hours to finish the job.

The answer is '10'

Choice D is the correct answer.

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