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:

(1)17 (2) 20
(3) 25 (4) 27 (5) 30

Solution follows here:

Let the number of days
required to finish the job with all the 150 workers engaged all the days be ‘n’

=> man-days required to complete the job =
150*n --(1)

Number of workers on
day-1 = 150

4 workers dropped out on
second day => Number of workers on day-2 = 150-4 = 146

4 more workers dropped
out on third day => Number of workers on day-3 = 146-4 = 142

In this scenario, it required
to complete 8 more days => (n+8) days

Arranging number of
workers/ each day in an order,

150, 146, 142,…… (n+8)
terms

This is a decreasing A.P,
with initial term = a = 150; and common difference = d = -4;

Sum to (n+8) terms = S

_{n+8}= (n+8)/2 * (2a+(n+8-1)d)
= (n+8)/2 * (300-4(n+8-1))
= (n+8)(136-2n) --(2)

This is nothing but the man-days
calculated in (1),

=> (n+8)(136-2n) =
150n => (n+8)(68-n) = 75n => 68n+544-n

^{2}-8n = 75n
=> n

^{2}+15n-544 = 0 => n^{2}+32n-17n-(17*32) = 0 => n(n+32)-17(n+32)=0
=> n = 17 (or) -32, we
can leave out negative values as this represents number of days

=> n=17

Wait a minute, this is
not the answer. We assumed ‘n’ to be number of days to finish the job when all
150 workers engaged for all the days. But in the actual scenario, it took

**(n+8)**days due to gradual dropping out of workers on each day.
Answer =

**n+8**= 17+8 =**25****Answer (3)**
## No comments:

## Post a Comment