50 people can complete a piece of work in 30 days. If half workers left after completion of one-fifth of work, find the time taken in completing the work completely.

- 50 days
- 35 days
- 54 days
- 20 days

Option 3 : 54 days

**Given:**

50 people can complete a piece of work in 30 days.

Half workers left after completion of one-fifth of work.

**Concepts used:**

Time = Work/Efficiency

Total Work = Number of days × number of people

**Calculation:**

Total Work done by 50 people in 30 days = 50 × 30 = 1500 unit

(1/5)th of work completed by 50 people = 1500 × 1/5 = 300 unit

⇒ Number of days taken to complete (1/5)th of work^{ } = 300/50 ⇒ 6 days

Remaining work = 1500 - 300 = 1200 unit

Number of workers left = 50/2 = 25 workers

Remaining workers = 50 - 25 = 25

Number of days taken by remaining workers to complete remaining work = 1200/25 ⇒ 48 days

⇒ Total number of days worked = 48 + 6 = 54 days

**∴ Total work gets completed in 54 days**.

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