Total number of workers = 150 Number of workers on 2nd day = 150 – 4 = 146 Number of workers on 3rd day = 146 – 4 = 142 So, the number of workers will be like 150, 146, 142, ..... Let 150 workers take n days to complete the work, then one worker will complete the work in 150n days. On decreasing the numbers of workers it takes 8 days more to finish the work, then 150 + 146 + 142 + ..... to (n + 8) terms = 150 n ⇒ $\frac{n+8}{2}$ [2 × 150 + (n + 8 - 1) (- 4)] = 150n ⇒ $\frac{n+8}{2}$ [300 - 4n - 28] = 150n ⇒ (n + 8) [272 – 4n] = 300 n ⇒ 272n – $4n^2$ + 2176 – 32n = 300n ⇒ – $4n^2$ – 60n + 2176 = 0 ⇒ $n^2$ + 15n – 544 = 0 ⇒ (n – 17) (n + 32) = 0 ⇒ n = 17, – 32 n ≠ – 32, because number of days cannot be negative. ∴ n = 17. So, the work was completed in (17 + 8) i.e., 25 days.