CAT 2017 Slot 1 — QA Question 2

Let the number of days required to complete the job be n.

1 person works on day 1, 2 on day 2, 3 on day 3, …. n on day n.

Using Unitary Method:
Each person has the same efficiency = $\frac{1}{120}$

Work done on
Day 1 = $1\times \frac{1}{120}$
Day 2 = $2\times \frac{1}{120}$
...
Day n = $\mathrm{n}\times \frac{1}{120}$

∴ Total Work = $1\times \frac{1}{120}$ + $2\times \frac{1}{120}$ + ... + $\mathrm{n}\times \frac{1}{120}$

This is also equal to 1.

∴ $\frac{1}{120}+\frac{2}{120}+\frac{3}{120}+..+\frac{n}{120}$ = 1

∑n = 120
⇒ $\frac{\mathrm{n}(\mathrm{n}+1)}{2}$ = 120
⇒ n = 15

Hence, 15.