A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days t

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Solution

Q.
A software company sets up $m$ number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of $m$ is equal to: [2024]

1 160

2 180

3 150

4 125

Ans.
(3)

Let the work done by each computer $= k$

$∴$ Total work $= 17$ $m k$

Work done on 1 day by $m$ computers $= m k$

Work done on day 2 by $m - 4$ computers $= (m - 4) k$

Work done on day 3 by $m - 8$ computers $= (m - 8) k$

Work done on day 25 $= (m - (24 \times 4)) k$

$= (m - 96) k$

$∴$ $m k + (m - 4) k + \dots + (m - 96) k = 17 m k$

$\Rightarrow 25 m - (4 + 8 + \dots + 96) = 17 m$

$\Rightarrow 8 m = \frac{24}{2} (4 + 96) \Rightarrow m = 150$

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