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A **contractor** employed **150 labourers** to finish a peice of work in a certain no. of days.** 4 workers **went away the **second day**, **4 more workers** went away the **third day** and **so on**. If **it took 8 more days** to finish the work , **find the no. of days in which the work was completed.**

**ANURAG.**

A **contractor** employed **150 labourers** to finish a peice of work in a certain no. of days.** 4 workers **went away the **second day**, **4 more workers** went away the **third day** and **so on**. If **it took 8 more days** to finish the work , **find the no. of days in which the work was completed. **

**ANURAG.**

Suppose the work is completed in *n* days.

Since 4 workers went away on every day except the first day.

∴ Total number of worker who worked all the *n* days is the sum of n terms of A.P. with first term 150 and common difference – 4.

Total number of worker who worked all the *n* days

If the workers would not have went away, then the work would have finished in (*n* – 8) days with 150 workers working on every day.

∴ Total number of workers who would have worked all *n* days = 150 (*n* – 8)

∴* n* (152 – 2*n*) = 150 (*n* – 8)

⇒ 152*n* – 2*n*^{2} = 150*n* – 1200

⇒ 2*n*^{2} – 2*n* – 1200 = 0

⇒ *n*^{2} – *n* – 600 = 0

⇒ *n*^{2} – 25*n* + 24*n* – 600 = 0

⇒ *n*(*n* – 25) + 24 (*n* + 25) = 0

⇒ (*n* – 25) (*n* + 24) = 0

⇒ *n* – 25 = 0 or *n* + 24 = 0

⇒ *n* = 25 or *n* = – 24

⇒ *n* = 25 (Number of days cannot be negative)

Thus, the work is completed in 25 days.

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