CAT 2022 Slot 3 QA Question 16: Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work toge

Question

Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work toge

Accepted Answer

Take Alex, Bob and Cole’s efficiencies in the ratio $6 : 3 : 2$. This satisfies the conditions that Alex is twice as fast as Bob and thrice as fast as Cole.
Since Bob alone takes 40 days, total work is
$40 	imes 3 = 120$ units
Work done in one 3-day cycle is
$(	ext{Alex} + 	ext{Bob}) + (	ext{Bob