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

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 — Easy Everyone has the same rate $	frac1{120}$ per day. With $k$ workers on day $k$, the work done on day $k$ is $	frac{k}{120}$. Sum the days until the total work equals $1$ &mdash; that turns into the sum $1+2+\dots+n$. 1 Work done each day. On day $k$ there are $k$ people, each doing $	frac1{120}$ of the job. $$\begin{aligned} &	ext{Day } k:\quad k	imes\frac{1}{120}=\frac{k}{120} \end{aligned}$$ 2 Total work over $n$ days equals $1$. Add days $1$ through $n$. $$\begin{aligned} &\frac{1}{1

CAT 2017 Slot 1 — QA Question 2

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