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Question

300 workers were engaged to finish a piece of work in a certain number of days. 8 workers dropped on the second day, 8 more workers dropped on the third day and so on. It took 8 more days to finish the work now. The number of days in which the work was completed is

A
35
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B
30
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C
25
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D
28
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Solution

The correct option is C 25
Let x be the number of days in which 300 workers completed the work.
According to the given information,
300x = 300 + 292 + 284 + … to (x + 8) terms
The series 300 + 292 + 284 + … to (x + 8) terms is an AP with first term as 300, common difference as –8 and number of terms as (x + 8).
The sum of n terms for an AP with first term a and common difference d is given by
Sn=n2[2a+(n1)d]
300x=x+82[2(300)+(x+81)×(8)]
300x×2=(x+8)[600+(x+7)×(8)]
600x=(x+8)(6008x56)
600x=(x+8)(5448x)
600x=x(5448x)+8(5448x)
600x=544x8x2+435264x
600x544x+64x+8x24352
8x2+120x4352=0
x2+15x544=0
x2+32x17x544=0
(x17)(x+32)=0
x=17 or x=32
∴ x = 17 (As x cannot be negative)
Thus, the number of days in which the work was completed is 17.
∴ Required number of days = 17 + 8 = 25
Hence, the correct answer is option (3).

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