Question
25 men can complete a piece of work in 13 days. One man
starts the work and after every day one more man joins the work and this continues till the work is completed. Then, in how many days will the work be completed?Solution
Let 1 day work of 1 man = 1 units So total work = 25 ×13 = 325 units Suppose after n days work is finished. So, 1 + 2 + ………… +n = 325 ⇒ (n(n+1))/2 = 325 n² + n – 650 = 0 n² + 26n – 25n – 650 = 0 n(n + 26 ) – 25(n + 26) = 0 (n - 25)  (n + 26) ∴ n = 25 Hence, the work will be finished in 25 days.
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