# in How Many Days can A Alone do it? If

A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it?

- 80 days
- 100 days
- 120 days
- 150 days

**Answer: (3) 120 days**

**Explanation:-**

A and B can do a piece of work = 72 days

Therefore, A and B can do a piece of work in a day = 1/72.

B and C can do it = 120 days

Therefore, B and C can it in a day = 1/120

A and C can do it = 90 days

Therefore, A and C can do in a day = 1/90

Then, A , B & C can do it in a day = (1/72 + 1/120 + 1/90 ) / 2

= (5 + 3 + 4)/360 x 2

= 12 /360 x 2

= 1/30 x 2

= 1/60

Then, A alone can do it in a day = 1/60 – 1/120

= (2 – 1 ) /120

= 1/120

Therefore, A alone can do complete the work = 120 days.

Hence, the answer is (3) 120 days.