In the problem, it is stated that A and B together can complete the work in 5 days. Then it is stated that if A works at twice his speed and B at half his speed, they can finish the work in 4 days. This implies that if A works at twice his speed, it compensates for B working at half his speed, and they finish the work a day earlier. Now, if both worked at their original speed for a day more, they could have finished the work. This implies that A, working twice as fast as his normal pace can finish the work alone in 5 days. Thus, A working at his normal speed should take twice as long, i.e., 10 days to finish the work alone. Thus, the correct answer is Option 1: A needs 10 days to complete the work alone. Options 2, 3 and 4 suggesting 12, 15 and 18 days respectively are incorrect because these figures are longer than the combined effort of A and B, which doesn`t make sense considering A`s increased efficiency in the given scenario.