Question

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.

Answer 1

Let x be the number of days in which 150 workers finish the work.

Answer 2

Are you familiar with A.P ?

Answer 3

@Aditi_Singh

Answer 4

\[\frac{ n(2*150+(n-1)*-4) }{ 2 } =150(n-8)\]

Answer 5

Find n..)

Answer 6

Yep, ofcourse i know AP!

Answer 7

Let the work be completed in n days when 4 workers are dropped on every day except on the first day.
Since 4 workers are dropped on every day except on the first day, total number of man days who worked for n days is the sum of n terms of an A.P. with first term as 150 and common difference as –4.

The work would have finished in (n − 8) days with 150 workers when the number of workers are not drooped.
Total number of man days who would have worked at all n days = 150(n – 8)
∴n (152 – 2n) = 150(n – 8)
⇒152n – 2n 2 = 150n – 1200
⇒ 2n 2 –2n – 1200 = 0
⇒ n 2 – n – 600 = 0
⇒ (n – 25)(n + 24) = 0
⇒ n = 25 [n > 0]
Thus, the number days in which the work was to be completed is (25 – 8) = 17 days

Answer 8

ok @Aditi_Singh

Answer 9

got it @Aditi_Singh

Answer 10

no @mayankdevnani :(

Answer 11

I don't get that n-8 wala part!

Answer 12

answer is wrong

Answer 13

No, it's absolutely right!

Answer 14

ok @Aditi_Singh

Answer 15

@Yahoo! , How do you get tha n-8 part ?

@hba , Help me friend!

Answer 16

the question said it took 8 more Days....with 150 , 146 ...etc Workers on 1 st 2 2nd .....Days..... so if 150 Workers are working it would take n-8 days

Answer 17

so 17+8=25