150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

Question

Dr. Abubacker · Accepted Answer

(c)
Let the number of days be $n$. Hence, a worker can do $\left( \frac{1}{150n} ight)$th part of the work in day.
According to given condition
$(150 + 146 + 142 + ... +$upto $\begin{matrix}
(n + 8) \
terms
\end{matrix} 	imes \frac{1}{150n} = 1$
$\Rightarrow \ \ \frac{n + 8}{2}\left\lbrack 300 + (n + 8 - 1)( - 4) ightbrack = 1$
$\Rightarrow \ \ (n + 8)(272 - 4n) = 300n$
$\Rightarrow \ \ 4n^{2} + 60n - 2176 = 0$
$\Rightarrow \ \ n^{2} + 15n - 544 = 0$
$\Rightarrow \ \ n = 17,\  - 32$
We do not take negative value
$	herefore\ n = 17$
Therefore, number of total days
$= 17 + 8 = 25$

Q. 150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

Explanation

Reviewed by Dr. Abubacker

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