A software company sets up $m$ number of computer systems to finish an assignment in 17 days. If 4 computer…

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 $\mathrm{m}$ is equal to:
  1. 150
  2. 180
  3. 160
  4. 125

Solution

$\begin{aligned} & 17 \mathrm{~m}=\mathrm{m}+(\mathrm{m}-4)+(\mathrm{m}-4 \times 2) \ldots+\ldots(\mathrm{m}-4 \times 24) \\ & 17 \mathrm{~m}=25 \mathrm{~m}-4(1+2 \ldots 24) \\ & 8 \mathrm{~m}=\frac{4 \cdot 24 \cdot 25}{2}=150\end{aligned}$

Asked in: JEE Main 2024 (06 Apr Shift 2)

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