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# CAT 2021 Quant Question [Slot 1] with Solution 17

Question
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
Option: 32
Solution:
Let the total work be 48 units. Let Amar do 'm' work, Akbar do 'k' work, and Anthony do 'n' units of work in a month.
Amar and Akbar complete the project in 12 months. Hence, in a month they do $\frac{{48}}{{12}}$=4 units of work.
m+k = 4.
Similarly, k+n = 3, and m+n = 2.
Solving the three equations, we get $m = \frac{3}{2},\;k = \frac{5}{2},\;n = \frac{1}{2}$.
Here, Amar works neither the fastest not the slowest, and he does 1.5 units of work in a month. Hence, to complete the work, he would take $\frac{{48}}{{1.5}} = 32$ months.
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