Question

A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?

Accepted Answer

15. Let total work = 120 units. Each person does 1 unit per day. On Day 1: 1 unit On Day 2: 2 units ... On Day $n$: $n$ units. Total work in $n$ days = $1 + 2 + \dots + n = \frac{n(n+1)}{2}$. We require $\frac{n(n+1)}{2} = 120 \implies n(n+1) = 240$. Since $15 	imes 16 = 240$, $n = 15$.

Work Completion with Incrementing Workers

Explanation

Practise this under exam conditions