CAT 2021 Question Paper | Quant Slot 1

CAT Previous Year Paper | CAT Quant Questions | Question 12

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 12 : Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is

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Explanatory Answer

Let's consider the efficiencies of Amar, Akbar, and Anthony to be x, y, z respectively.
x + y = \\frac{1}{12})
y + z = \\frac{1}{16})
z + x = \\frac{1}{24})
If we add the above equations, we will get 2(x + y + z) = \\frac{3}{16})
x + y + z = \\frac{3}{32})
From the above equations, we can get x = \\frac{1}{32}), y = \\frac{5}{96}), z = \\frac{1}{96})
Hence, x is neither the fastest nor the slowest.
Amar can complete the project in 32 months.

The answer is '32'

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