CAT 2021 Slot 1 QA Question 9: 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 ye

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 ye

Accepted Answer

Convert all times to months. Let the monthly work rates of Amar, Akbar and Anthony be $A$, $B$ and $C$ respectively.
$A+B = \dfrac{1}{12}, \quad B+C = \dfrac{1}{16}, \quad C+A = \dfrac{1}{24}$
Adding the three equations,
$2(A+B+C) = \dfrac{1}{12} + \dfrac{1}{16} + \dfrac{1}{24} = \dfrac{3}{16}$
$A+B