Question

150 workers were engaged to finish a piece of work in a certain number of days. Four workers stopped working on the second day, four more workers stopped their work on the third day and so on. It took 8 more days to finish the work. Then the number of days in which the work was completed is

• A. 29 days
• B. 24 days
• C. 25 days
• D. none of these

Answer 1

The correct option is C

25 days

Suppose the work is completed in n days when the workers stopped working. Since four workers stopped working every day except the first day. Therfore, the total number of workers who worked all the n terms of an A.P. with first term 150 and common difference -4, i.e.,
$\frac{n}{2}[2\times 150+(n-1)\times -4]=n(152-2n)$
Had the workers notstopped working, then the work would have finished in (n-8) days with 150 workers working on each day. Therfore, the total number of workers who would have worked all the n days is 150 (n-8)
$\therefore n(152-2n)=150(n-8)$

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

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

$\Rightarrow n=25$

Thus, the work is completed in 25 days.