A software company sets up m number of computer systems... | Sequence & Series (Mathematics)

JEE Mains 2024 6th April Shift 2

Mathematics

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 n 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

160

180

150

125

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Correct Answer:

150

Explanation

= k

\\

\therefore

Total work

= 17mk

\\

Work done on 1 day by

m

computers

= mk

\\

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

\therefore\ mk + (m - 4)k + \ldots\ldots.. + (m - 96)k = 17mk

\Rightarrow 25m - (4 + 8 + \ldots.. + 96) = 17m

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

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Explanation

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