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, every day a new person with the same efficiency joins the work. How many days are required to complete the job?

a) 45
b) 59
c) 60
d) 61

Answer 1

It takes 120 days for the group to complete the job.

Step-by-step explanation:

To solve this problem, we need to find the number of days it takes for the group to complete the job when each new person joins. Since each person can complete the job in 120 days, we can say that on each day, the group completes 1/120th of the job. On day 1, the first person completes 1/120th of the job. On day 2, the second person joins and together they complete 2/120ths of the job. On day 3, the third person joins and together they complete 3/120ths of the job. We can generalize this pattern to say that on day N, N/120th of the job is completed. So, we need to find the value of N that makes N/120 equal to 1. To do this, we can set up the equation N/120 = 1 and solve for N:

N = 120

Therefore, it takes 120 days for the group to complete the job.