a person can complete a job in 120 days he works alone on day 1.on day 2 He is joined by another person who also can complete the job in exactly 120 days on day3 they are joined by the another person of equal efficiency like this everyday new person with the same efficiency Joins the work how many days are required to complete the job ?
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As per the question from CAT 2017 – Quantitative Aptitude – Arithmetic – Time and Work, we can see that,
On Day 1, the person works alone. So, work done on Day 1 = 1/120
Next day, another person joins him, Work done on Day 2 = 2/120
And so on, until the final day
So, sum total of work done = 1/120 + 2/120 +………+ n/120 = 1
(1/120) (1 + 2+3+……+n) = 1
(1/120) [n(n+1)/2] = 1 (Sum of n positive integers)
On solving, we get n = 15.
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