Correct Answer:

D: 30 days

Explanation of Statements/Options:

Option A: 20 days  
 • Incorrect.
 • If A alone could complete the work in 20 days, then A's work rate would be 1/20 of the work per day.
 • Together, A and B complete the work in 10 days, so their combined work rate is 1/10 of the work per day.
 • B's work rate is 1/15 of the work per day. Adding A's and B's rates should equal the combined rate: 1/20 + 1/15 ≠ 1/10.

Option B: 24 days  
 • Incorrect.
 • If A alone could complete the work in 24 days, then A's work rate would be 1/24 of the work per day.
 • Adding A's and B's rates: 1/24 + 1/15 ≠ 1/10, which does not match the combined rate of A and B.

Option C: 25 days  
 • Incorrect.
 • If A alone could complete the work in 25 days, then A's work rate would be 1/25 of the work per day.
 • Adding A's and B's rates: 1/25 + 1/15 ≠ 1/10, which does not match the combined rate of A and B.

Option D: 30 days  
 • Correct.
 • If A alone can complete the work in 30 days, then A's work rate is 1/30 of the work per day.
 • Adding A's and B's rates: 1/30 + 1/15 = 1/10, which matches the combined rate of A and B working together.
 • Therefore, A alone can finish the work in 30 days.