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8. Sequences and Series
medium
$150$ 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
A
$15$
B
$20$
C
$25$
D
$30$
Solution
(c) Let the number of days be $n$.
Hence a worker can do ${\left( {\frac{1}{{150n}}} \right)^{th}}$ part of the work in a day.
Accordingly,
$[150 + 146 + 142 + ……. + {\rm{upto}}\;(n + 8)\,{\rm{terms}}] \times \frac{1}{{150n}} = 1$
$ \Rightarrow $$n = 17$
Therefore number of total days in completion $ = 17 + 8 = 25$.
Standard 11
Mathematics
