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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 From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. The total work done is equal to 55% of square of the total number of workers working initially. How many workers are there in the group?

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 From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. The total work done is equal to 55% of square of the total number of workers working initially. How many workers are there in the group? Correct Answer 10

Let there are n workers in the group

According to the question,

Every day one worker withdrawn and when the work was done, last worker was withdrawn

⇒ Work done = n + (n – 1) + (n – 2) + … + 3 + 2 + 1 = 1 + 2 + 3 + … + n

⇒ Work done = n(n + 1)/2

Also,

If all workers were there, the group would have finished the work in 55% of the time

⇒ Work done = n × 55% of n

⇒ Work done = n × 55n/100

So,

⇒ n(n + 1)/2 = n × 55n/100

⇒ 100n + 100 = 110n

⇒ n = 10

∴ There are 10 workers in the group

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