Explanation:

Let’s break it down:

- A and B finish the work in 15 days. So together, they do 1/15 of the work per day.

- B and C get it done in 20 days. So their combined rate is 1/20 per day.

- A and C, working together, finish in 30 days. That’s 1/30 per day.

If you add those up:

(1/15) + (1/20) + (1/30) = (4 + 3 + 2) / 60 = 9/60 = 3/20

But notice: This actually adds everyone's rate twice (because each pair includes two people). So to get the total rate of A+B+C:

(A+B) + (B+C) + (A+C) = 2(A+B+C)

So, 2(A + B + C) = 3/20 ? (A + B + C) = 3/40

That means, all three together do 3/40 of the work per day. So to complete the full work:

1 / (3/40) = 40/3 days

Now, looking at the options:

- Option 1: 45/6 = 7.5 days (doesn’t match)

- Option 2: 32/5 = 6.4 days (nope)

- Option 3: 38/4 = 9.5 days (nope)

- Option 4: 40/3 ˜ 13.33 days (this is the right one)

- Option 5: None of these (not needed)

So your answer is:

Option 4 – 40/3 days