CAT 2021 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 6

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 6 : Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of ₹ 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is

  1. 9000
  2. 9100
  3. 9200
  4. 9150

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Explanatory Answer

Anil can paint a house in 60 days. So, he can do \\frac{1}{60}) of work per day.
Bimal can paint it in 84 days. So, he can do \\frac{1}{84}) of work per day.
Let’s assume charu can paint it in ‘c’ days. So, he can do \\frac{1}{c}) of work per day.
Anil alone does the work for 10 days. So, the work completed is \\frac{1}{6})
The remaining work is \\frac{5}{6}).
After that, for 14 days they worked together.
\\frac{14}{60})+ \\frac{14}{84}) + \\frac{14}{c}) = \\frac{5}{6})
\\frac{1}{c}) = \\frac{13}{30 \times 14})
Charu does his work for 14 days. So, the total work done by charu is \\frac{13}{30}).
The amount earned by charu = \\frac{13}{30}) x 21000 = Rs 9100

The answer is '9100'

Choice B is the correct answer.

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