A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last wor… — Answer & Discussion

A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?

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Discussion 1

CCommunity15 Jun 2019

Let n be the number of workers and x be the work done by 1 worker in 1 day

∴ According to the 1st condition,

⇒ nx + (n - 1)x + (n - 2)x + … + x = 1

∴ x × n(n + 1)/2 = 1

∴ x × n(n + 1) = 2 - - - - - (1)

Also According to the 2nd given condition,

(55n/100) × nx = 1

∴ x = 20/(11 × n × n) - - - - - (2)

On substituting (2) in (1) we get,

20/11n2 × (n2 + n) = 2

(n2 + n)/n2 = 11/10

1 + 1/n = 11/10

∴ n = 10

∴ There are 10 workers in the group.