The Senate education subcommittee has trimmed a big House-passed college aid bill back toward balanced budget-year size by cutting out an estimated $15 billion in student aid over the five-year life of the program.

Under present law, federal grants to needy college students are limited to 50 percent of college costs up to $1,800 a year. Expensive private colleges, which cost $8,000 and up, want the dollar ceiling raised, while less expensive public colleges would be helped by raising the percentage ceiling.

The House resolved this struggle by raising both and sent the bill to the Senate last year with the backing of most colleges. The grant ceilings would rise to 70 percent but not more than $2,520 a year by 1985. But the administration said that would cost too much and the Senate subcommittee agreed. The Congressional Budget Office estimated college student aid would rise to $11 billion a year by 1985.

The Senate subcommittee raised both percentage and dollar limits but by lesser amounts that are expected to cost an average of $3 billion a year less than the House bill. The Senate bill would increase the percentage limit to 60 percent. The cash limits would go up at a slower rate through 1984, but would jump ahead to a maximum of $2,600 in 1985.

The Senate bill would also increase the interest rate on subsidized college student loans from 7 to 9 percent.

The full Senate Human Resources Committee will take up the bill at the end of this month. Under the Congressional Budget Act, it must be cleared to the Senate floor by May 15.