VerifiedHint: If you look at the given data, it gives you an idea that it is in a sequence. Observe the difference in the series and apply appropriate formulas related to that series, you’ll get the answer.
Complete step by step answer:
As we know,
Total numbers of workers day = 150
Except for the first day,everyday 4 workers left the job.
So,second day number of workers = 146
Third day number of workers = 142
And this continued till n number of days
As we know the formula,
Sum of n terms in AP, $S = n/2[2a + (n - 1)*d]$
So,total work = $n/2[2a + (n - 1)*d]$
Here, a = 150, d = - 4
Putting these values in the above equation,we get
Total work = $n/2[2*150 + (n - 1)( - 4)]$
= $(152n - 2{n^2})$ (Eq 1)
If all the 150 workers are working for n days
Then,total work = 150(n - 8) (Eq 2)
Comparing both (1) and (2), we get,
$152n - 2{n^2} = 150(n - 8)$
$\Rightarrow$ $152n - 2{n^2} = 150n - 1200$
$\Rightarrow$ $152n - 150n - 2{n^2} = - 1200$
$\Rightarrow$ $2{n^2} - 2n - 1200 = 0$
$\Rightarrow$ ${n^2} - n - 600 = 0$
$\Rightarrow$ $(n - 25)(n + 24) = 0$
$\Rightarrow$ n = 25,n = - 24
As we know,the number of days cannot be negative.
So,number of days = 25
This is the required answer.
Note: In these types of questions ,we have to check whether a series is being used or not. If a series is being used , we have to find whether it is AP or GP and then calculate the solution.
