NCERT Solutions
Class 11 Maths
Sequences and Series

Ex.Misc.Q.32
150 workers were engaged to finish a job in a certain number of days.
4 workers dropped out on second day, 4 more workers dropped out on 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 x be the number of days in which 150 workers finish the work.
According to the given information,
150x = 150 + 146 + 142 + …. (x + 8) terms
The series 150 + 146 + 142 + …. (x + 8) terms is an A.P. with first term 146, common difference –4 and number of terms as (x + 8)
=> 150x = {(x + 8) ÷ 2} [2 × 150 + (x + 8 - 1) (-4)]
=> 150x = (x + 8) [150 + (x + 7) (-2)]
=> 150x = (x + 8) [150 - 2x - 14]
=> 150x = (x + 8) [136 - 2x]
=> 75x = (x + 8) (68 – x)
=> 75x = 68x – x2 + 544 – 8x
=> x2 + 75x - 60x – 544 = 0
=> x2 + 15x – 544 = 0
=> x2 + 32x - 17x – 544 = 0
=> x (x + 32) – 17(x + 32) = 0
=> (x + 32) (x - 17) = 0
=> x = -32, 17
However, x cannot be negative.
So, x = 17
Therefore, originally, the number of days in which the work was completed is 17.
Thus, required number of days = (17 + 8) = 25