Question

300 workers were engaged to finish a piece of work in a certain number of days. 8 workers dropped on the second day, 8 more workers dropped on the third day and so on. It took 8 more days to finish the work now. The number of days in which the work was completed is

• A. 35
• B. 30
• C. 25
• D. 28

Answer 1

The correct option is C 25

Let x be the number of days in which 300 workers completed the work.
According to the given information,
300x = 300 + 292 + 284 + … to (x + 8) terms
The series 300 + 292 + 284 + … to (x + 8) terms is an AP with first term as 300, common difference as –8 and number of terms as (x + 8).
The sum of n terms for an AP with first term a and common difference d is given by
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$\Rightarrow 300x=\frac{x+8}{2}\left[2\right(300)+(x+8-1)\times (-8\left)\right]$
$\Rightarrow 300x\times 2=(x+8)[600+(x+7)\times (-8\left)\right]$
$\Rightarrow 600x=(x+8)(600-8x-56)$
$\Rightarrow 600x=(x+8)(544-8x)$
$\Rightarrow 600x=x(544-8x)+8(544-8x)$
$\Rightarrow 600x=544x-8x^2+4352-64x$
$\Rightarrow 600x-544x+64x+8x^2-4352$
$\Rightarrow 8x^2+120x-4352=0$
$\Rightarrow x^2+15x-544=0$
$\Rightarrow x^2+32x-17x-544=0$
$\Rightarrow (x-17)(x+32)=0$
$\Rightarrow x=17$ or $x=-32$
∴ x = 17 (As x cannot be negative)
Thus, the number of days in which the work was completed is 17.
∴ Required number of days = 17 + 8 = 25
Hence, the correct answer is option (3).