Question : A group of workers can complete a piece of work in 50 days when they are working individually. On the first day one person works, on the second day, another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many approximate days are needed to complete the work?
Option 1: 8 days
Option 2: 9 days
Option 3: 10 days
Option 4: 11 days
Correct Answer: 10 days
Solution :
Let the total work be 50 units and let a man complete 1 piece of work in a day.
Work done on 1st day = 1 man × 1 work/day = 1 unit of work
Work done on 2nd day = 2 men × 1 work/day = 2 units of work
Work done on 3rd day = 3 men × 1 work/day = 3 units of work
Let the whole work will be completed in $N$ days.
So, total work 1 + 2 + 3 + ..... + $N$ = 50
$\frac{N(N+1)}2=50$
⇒ $N(N + 1) = 100$
⇒ $N=10$ days(approx)
Hence, the correct answer is 10 days.
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