Question

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day,4 more on workers dropped out on third day and so on. It took 8 more days to complete the work. Find the number of days in which the work was completed.

Answer 1

Sol: Suppose the work is completed in n days.

Since 4 workers went away on every day except the first day.

∴ Total number of worker who worked all the n days is the sum of n terms of A.P. with first term 150 and common difference – 4.

Total number of worker who worked all the n days = n/2[2 x 150 + (n-1) x -4 ] = n (152 – 2n)

If the workers would not have went away, then the work would have finished in (n – 8) days with 150 workers working on every day.

∴ Total number of workers who would have worked all n days = 150 (n – 8)

∴ n (152 – 2n) = 150 (n – 8)

⇒ 152n – 2n2 = 150n – 1200

⇒ 2n2 – 2n – 1200 = 0

⇒ n2 – n – 600 = 0

⇒ n2 – 25n + 24n – 600 = 0

⇒ n(n – 25) + 24 (n + 25) = 0

⇒ (n – 25) (n + 24) = 0

⇒ n – 25 = 0 or n + 24 = 0

⇒ n = 25 or n = – 24

⇒ n = 25 ( Number of days cannot be negative)

Thus, the work is completed in 25 days.