TO say that La Salle College student To Tak-chi has worked against the odds and beaten them resoundingly would be an understatement. The science student, who lives with his unemployed widowed mother and two brothers on a social welfare allowance of $5,000 a month, emerged yesterday as one of the top brains in the territory, having scored the maximum 10 As in this year's Hong Kong Certificate of Education Examinations (HKCEE). In fact, 17-year-old Tak-chi said he believed that not being as affluent as his schoolmates might actually have helped him achieve his excellent results. ''Since we are still struggling to pay for the monthly payment of our flat in Sha Tin and my mother can't get a job, there is not much entertainment for us,'' Tak-chi said. ''No entertainment means no distraction. It allows me to focus on my studies with solid determination.'' This year, 120,555 candidates sat for the HKCEE and a record-breaking eight - all of them male - scored the maximum 10 distinctions. Queen's College claimed four of the other 10-As students, two came from Wah Yan College and one from King's College. Since the Hong Kong Examinations Authority allowed students to take a maximum of 10 subjects in 1987, the number of 10-As students has increased steadily from one in 1987 to six last year. Tak-chi lost his father when he was eight. The family has been receiving social welfare since shortly after he died. But with brothers in Form Four and Primary Six, Tak-chi fears his weak financial situation might hamper his further education. ''I'm afraid that I will have to find myself some part-time jobs if my family can't afford my matriculation expenses,'' he said. One of Tak-chi's classmates said: ''He is always the most quiet and shy one in the crowd and maybe that explains why he is always contemplative.'' Although Tak-chi has no firm career plans, he hopes to work in the finance and economics sector. ''Frankly, I would like to study abroad and gain new experiences. But my family cannot afford it,'' he said. ''But pursuing my education in Hong Kong is not exactly an unattractive prospect.''