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

Solution:

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

Here, 150 + 146 + 142 + ..... (x + 8) terms forms an A.P. with a = 146, d = - 4, n = ( x + 8)

Using the sum of n terms of A.P. formula,

⇒ 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)

Dividing both sides by 2,

⇒ 75x = (x + 8)(68 - x)

⇒ 75x = 68x - x² + 544 - 8x

⇒ x² + 15x - 544 = 0

⇒ x² + 32x - 17x - 544 = 0

⇒ x (x + 32) - 17 (x + 32) = 0

⇒ (x - 17)(x + 32) = 0

⇒ x = 17, - 32

However, x cannot be negative, hence, x = 17

Therefore, the number of days in which the work was completed is (17 + 8) = 25 days.

Thus, the work was completed in 25 days

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NCERT Solutions Class 11 Maths Chapter 9 Exercise ME Question 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

Solution:

If 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 and if it took 8 more days to finish the work then the number of days in which the work was completed is 25 days