CAT 2021 Slot 1 · Quant · Question 19
CAT 2021 Slot 1 previous year question on Time and Work, with the answer and a step-by-step solution.
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
Answer & solution
Answer: 32
Take the total work as 48 units.
Per month, Amar and Akbar do \frac{48}{12}=4 units, Akbar and Anthony do \frac{48}{16}=3 units, and Anthony and Amar do \frac{48}{24}=2 units.
Adding these, twice the combined rate is 4+3+2=9, so all three together do 4.5 units a month.
Hence Amar does 4.5-3=1.5, Akbar does 4.5-2=2.5 and Anthony does 4.5-4=0.5 units a month.
Amar is neither fastest nor slowest, and takes \frac{48}{1.5}=32 months.
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