(Q6).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 =
x+8
2
 [2 × 150 + (x + 8 - 1)(-4)]

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,

Sn =
n
2
 [2a + (n - 1)d]
=
x+
2
 [2 × + (x + - 1)(-)]
=
x+
2
 [ - x - ]
=
x+
2
 [ - x]

= (x + ) ( – x)

= -x2 + x + – x

= -x2 + x +

∴ x = -x2 + x +

⇒ x2 + x – = 0

⇒ x2 + x – = 0

⇒ x2 + x – x – =0

⇒ (x + ) – (x + ) = 0

⇒ (x + ) (x – ) = 0

⇒ x + = 0 (or) x – = 0

⇒ x = – (or) x =

x can’t be .

∴ x = .

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