Question

150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped from the work in the second day. Four workers dropped in third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed. [Let the no.of days to finish the work is ‘x’ then 150x = \(\frac{x+8}{2}\)[2 × 150 + (x + 8 – 1) (-4)]

Answer 1

Given: Number of workers engaged initially = 150. 

4 workers were dropped each day. 

Let the total work was to be completed initially was in x days. 

∴ Work done by 150 workers in x days = 150.x. 

But due to the dropping of 4 workers each day it took 8 more days. 

Work done in this case is 

150 × 1 + 146 × 1 + 142 × 1 + …. (x + 8) terms,

= (x + 8) (136 – 2x) 

= -2x² + 136x + 1088 – 16x

= -2x² + 120x + 1088 

∴ 150x = -2x² + 120x + 1088 

⇒ 2x² + 30x – 1088 = 0 

⇒ x² + 15x – 544 = 0 

⇒ x² + 32x – 17x – 544 =0 

⇒ x(x + 32) – 17 (x + 32) = 0 

⇒ (x + 32) (x – 17) = 0 

⇒ x + 32 = 0 (or) x – 17 = 0 

⇒ x = – 32 (or) x = 17 

x can’t be negative. 

∴ x = 17. 

i.e., The total work was completed in x + 8 days 

= 17 + 8 = 25 days.