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?
Explanation:
Let John’s efficiency be 1 unit/day.
∴ Jack’s efficiency is 2 units/day.
Jack and Jim’s efficiency is thrice John’s efficienc.
∴ 2 + eJim = 3 × 1
⇒ eJim = 1
John takes three days more than that taken by three of them working together
Let the time taken by all three together is d.
∴ Total work to be done = 4 × d = 1 × (d + 3)
⇒ d = 1
∴ Jack finished the work in d + 3 = 4 days.
Since, Jack and Jim have same efficiency, Jim will also finish the work in 4 days.
Hence, 4.
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