CAT 2020 Exam Shift 2 Solved Paper

Question : 54 of 76

Marks: +1, -0

John takes twice as much time as Jack to finish a job. Jack and Jim together take one thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?

Your Answer:

Validate

Solution:

Let the individual times taken by John, Jack and Jim to complete the works be

a, b

and

c

respectively.
Given,

a=2 b ⋅s(1)

\;{b c}/{b+c}=\;{1}/{3}(a) ⋅s(2)

a-(\;{a b c}/{a b+b c+a c})=3 ⋅s(3)

From

(1)

and

(2)

, we've

c=2 b

∴ 2 b-(\;{2 b × b × 2 b}/{(2 b)(b)+b(2 b)+(2 b)(2 b)})=3

⇒ b=2

∴ c=4

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