CAT 2024 Slot 3 QA Question 5: Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work togeth

Question

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work togeth

Accepted Answer

Let the total work be $1$ unit. The daily work rates are:

Sam = $\dfrac{1}{20}$
Mohit = $\dfrac{1}{10}$
Ayna = $\dfrac{1}{30}$

In one full 3-day cycle, the work done is:

$(S + M) + (S + A) + (M + A) = \dfrac{3}{20} + \dfrac{1}{12} + \dfrac{2}{15}$
Work in one cycle = $\dfrac{9 + 5 + 8}{60}$
Work