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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 25Let 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+(n−1)d] ⇒300x=x+82[2(300)+(x+8−1)×(−8)] ⇒300x×2=(x+8)[600+(x+7)×(−8)] ⇒600x=(x+8)(600−8x−56) ⇒600x=(x+8)(544−8x) ⇒600x=x(544−8x)+8(544−8x) ⇒600x=544x−8x2+4352−64x ⇒600x−544x+64x+8x2−4352 ⇒8x2+120x−4352=0 ⇒x2+15x−544=0 ⇒x2+32x−17x−544=0 ⇒(x−17)(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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