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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.


1. 50 days
2. 35 days
3. 54 days
4. 20 days

1 Answer

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Correct Answer - 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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