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 person joins them and this process continues till the work is completed. How many approximate days are needed to complete the work ?

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 person joins them and this process continues till the work is completed. How many approximate days are needed to complete the work ? Correct Answer 10 days

Let a man complete 1 piece of work in a day.
Then total work = 50 units
Then by statement 1 st day = one man × 1 work/day = 1
Then by statement 2nd day = two men × 1 work/day = 2
Then by statement 3rd day = three men × 1 work/day = 3
Let the whole work will be completed in N days.
Then total work 1 + 2 + 3 + ..... + N = 50
$$\eqalign{ & \frac{{{\text{N}}\left( {{\text{N}} + {\text{1}}} \right)}}{2} = 50 \cr & {\text{N}}\left( {{\text{N + 1}}} \right){\text{ = 100}} \cr & {\text{Then, N}} = 10{\text{ days}}\left( {{\text{approx}}} \right) \cr} $$
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