JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Sequences and Series

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A software company sets up m number of computer system 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

(A)125
(B)180
(C)160
(D)150✓ Correct

Answer: (D)

Solution

The job originally needs

m

machines for

17

days, i.e.

17 m

machine-days of work, and actually finishes in

17 + 8 = 25

days with

m - 4 (k - 1)

machines running on day

k

(

k = 1, \dots, 25

). Equating total work:

k = 1 \sum 25 [m - 4 (k - 1)] = 25 m - 4 (0 + 1 + \dots + 24) = 25 m - 1200 = 17 m \Rightarrow 8 m = 1200 \Rightarrow m = 150

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Single correct option

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