Question

There is a group of persons each of whom can complete a piece of work in 16 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 days are needed to complete the work?​

Answer 1

Answer :-

Let us assume that, total work to be done is 16 units .

so,

→ Work done by each person in a day = 16/16 = 1 unit/day .

then,

→ First day one person completes = 1 unit of work.

→ second day two person completes = 1 * 2 = 2 unit of work.

→ third day three person completes = 3 * 1 = 3 unit of work.

→ fourth day four person completes = 4 * 1 = 4 unit of work.

→ fifth day five person completes = 5 * 1 = 5 unit of work.

now,

→ work completed in 5 days = 1 + 2 + 3 + 4 + 5 = 15 units .

therefore,

→ Left work to be done = 16 - 15 = 1 units .

and,

→ Next day number of persons are = 6

hence,

→ Time taken by 6 persons to complete left work = (1/6) days.

then,

→ Total number of days = 5 + (1/6) = 5(1/6) days (Ans.)

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