Explanation:

Alright, let’s break this down:

- A + B complete the work in 15 days ? their combined 1 day work = 1/15

- B + C do it in 12 days ? combined 1 day work = 1/12

- C + A do it in 10 days ? combined 1 day work = 1/10

Let’s figure out everyone’s individual work per day:

Add up all three:

(A+B) + (B+C) + (C+A) = 1/15 + 1/12 + 1/10

Which simplifies to: 2(A+B+C) = (1/15 + 1/12 + 1/10)

Find the common denominator (60):

1/15 = 4/60, 1/12 = 5/60, 1/10 = 6/60

So, 2(A+B+C) = (4+5+6)/60 = 15/60 ? (A+B+C) = 15/120 = 1/8 per day.

If they all work together for 5 days, they do:

5 × 1/8 = 5/8 of the work.

So, what’s left? 1 – 5/8 = 3/8 of the work.

Now only A is left to finish.

A’s individual work per day?

A = (A+B+C) – (B+C)

We already have (A+B+C) = 1/8 per day

(B+C) = 1/12 per day

So, A = 1/8 – 1/12 = (3–2)/24 = 1/24 per day.

A finishes 1/24 of the work per day.

Work left: 3/8

Time taken = (3/8) ÷ (1/24) = (3/8)×24 = 9 days.

So the answer is Option 4 - 9 days.

- Option 1 (12 days): That's if A worked alone from start, but only the last chunk is left.

- Option 2 (4 days): Not enough time; that’s too little.

- Option 3 (15 days): That’s the time for A+B, not just A.

- Option 4 (9 days): That’s what the math gives us.

Nine days is correct. You nailed it!