Question

$300$ works were engeged to finish a piece of work in a certain number pf days. $8$ workers dropped on the second day, $8$ 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. $35$
• B. $30$
• C. $25$
• D. $28$

Answer 1

Answer: (C)

Suppose 1 worker does 1 unit work in a day

Assume 300 workers can finish the work in $(n-8)$ days, if all workers work all the days.

$\therefore$ total work $=300(n-8)..........\left(1\right)$

According to question, 300 workers work on day 1, 292 workers work on day 2, ... and work is completed in n days.

$\therefore$ total work $=300+292+...\left(\text{n terms}\right)$

This is an arithmetic progression with $a=300,\&d=-8$.

$\therefore$ total work $=\frac{n}{2}[2\times 300+(n-1)(-8)]$

$=\frac{n}{2}[600-8n+8]$

$=\frac{n}{2}[608-8n]$

$=n(304-4n)...\left(2\right)$

From $\left(1\right)\&\left(2\right)$, we have

$300(n-8)=n(304-4n)$

$75(n-8)=n(76-n)$

$75n-600=76n-n^2$

$n^2-n-600=0$

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

$n=25$

Hence, number of days in which the work was completed = 25.