Question

$150$ workers were engaged to finish a piece of work in a certain number of days. Four workers dropped the second day, four more workers dropped the third day and so-on. It takes $8$ more days to finish the work now. Find the number of days in which the work was completed.

• A. $24$ days
• B. $25$ days
• C. $26$ days
• D. $27$ days

Answer 1

Answer: (B)

$25$ days

Let the work can be completed in 'n' days

According to question

4 worker dropped out everyday except the first day.

Now,

Total number of worker who work on n days is the sum of 'n' term of A.P.

whose 1st term = $158$

common difference = -4

$\therefore$ Total number of worker who work on n days

$\Rightarrow \frac{n}{2}[2\times 150(n-1\left)\right(-4)$

$\Rightarrow n(152-2n)$

If 150 workers work on everyday then the work will be completed in $(n-8)$ days

$\therefore$ Total no of worker who work on n days $=150(n-8)$

$\therefore n(152-2n)=150(n-8)$

$\Rightarrow 152n-2n^2=150n-1200$

$\Rightarrow 2n^2-2n-1200=0$

$\Rightarrow n^2-n-600=0$

$\Rightarrow n^2-25n+24n-600=0$

$\Rightarrow n(n-25)+24(n-25)=0$

$\Rightarrow (n-25)(n+24)=0$

$\therefore n=25$ or $n=-24$

Taking positive terms

$n=25$

So, the work will be completed in $25$ days.