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Work Completion with Incrementing Workers

CAT 2017 Slot 1 · Quantitative Ability · Easy · Time and Work

This is an easy Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Time and Work. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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?

Answer

15

Explanation

Let total work = 120 units. Each person does 1 unit per day. On Day 1: 1 unit On Day 2: 2 units ... On Day nn: nn units. Total work in nn days = 1+2+⋯+n=n(n+1)21 + 2 + \dots + n = \frac{n(n+1)}{2}. We require n(n+1)2=120  ⟹  n(n+1)=240\frac{n(n+1)}{2} = 120 \implies n(n+1) = 240. Since 15×16=24015 \times 16 = 240, n=15n = 15.

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