Explanation:

Let's solve it step-by-step:

- Let total work = 1 unit.

- (A+B) can do in 25 days ? A+B’s 1 day work = 1/25

- (B+C) can do in 20 days ? B+C’s 1 day work = 1/20

- (C+A) can do in 10 days ? C+A’s 1 day work = 1/10

Adding all:

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

- So, (1/25) + (1/20) + (1/10) = 2(A+B+C)’s 1 day work

- Common LCM is 100 ? (4+5+10)/100 = 19/100

- So 2(A+B+C) = 19/100 ? (A+B+C) = 19/200 (per day)

- Therefore, all three together will finish the work in 1 / (19/200) = 200/19 days

- Now, matching with options:

- Option: 4, 200/19 days

- Option 1 (19/200 days): NOT correct. This is their combined 1 day work, not the total number of days.

- Option 2 (13/200 days): Incorrect, not derived in calculation.

- Option 3 (200/21 days): Incorrect.

- Option 5 (200/13 days): Incorrect.

- Option 4 (200/19 days) is the correct answer, which matches our calculation.