# CAT 2021 Exam Question Papers Slot 1 | CAT Quants

### CAT Quantitative Aptitude | CAT 2021 Question Papers

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All CAT 2021 Quantitative aptitude questions have detailed answer keys and solutions provided by our experts. Watch the videos below to learn the fastest ways to answer the questions:

2).

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

### Explanation

If Amar, Akbar and Anthony, working alone, complete the project in m, k and n months respectively, it is given that

1/m + 1/k  = 1/12     …….(1)

1/k + 1/n   = 1/16      ……(2)

1/n + 1/m  = 1/24      ……(3)

The person who is neither the fastest nor the slowest must appear in both the slowest and the fastest, i.e., in equations (3)  and  (1). So, Amar is neither the slowest

2 ( 1/m + 1/k + 1/n)  = 1/12 + 1/16 + 1/24 = (4 + 3 + 2)/48

= 9/48  = 3/16

=> 1/m + 1/k + 1/n   = 3/32                 …..(4)

Subtracting equation (2) from (4),

1/m = 3/32 – 1/16 =1/32

m = 32

Ans :(32)