The 10-cent transit fare paid by pupils who ride Metro's buses and trains to and from school in the District of Columbia is likely to be doubled by this fall, joining the three-cent letter and the five-cent candy bar as relics of a bygone era.

In addition to imposing a 20-cent school fare, the District government has announced plans to end the use of discount school tickets and tokens on weekends and during vacation periods, except by the relatively few pupils who actually are attending clases at those times.

For the parents who pay for sending an estimated 27,000 pupils to and from school on Metro vehicles, the higher fares would cost $36 a year for each child, bringing the total to about $72 a year.

The proposal to double school fares and to clamp down on the incidental use of discounts is another reflection of the District's budget crunch. The D.C. Department of Transportation estimated that, without a fare increase or restrictions, the city would overspend its $4.7 million budget for subsidizing reduced-fare school travel on Metro by nearly $1.9 million by the end of the fiscal year Sept. 30.

Under a law enacted by Congress in 1962, the District government is required to pay the transit system the difference between the school fare and the regular adult fare. When the law went into effect, the school fare -- then as now -- was 10 cents and the local bus fare was 25 cents, resulting in a 15-cent subsidy per trip. Adult fares have since risen to 60 cents while the school fare has remained static, pushing the current subsidy to 50 cents per trip.

Every time the Metro board raises transit fares for adults, it automatically triggers an increase in the city subsidy.

The District is the area's only political jurisdiction that provides subsidized fares for pupils who ride transit vehicles to school. Unlike the larger suburbs, however, the District does except for a few pupils attending specialized schools.

Legislation that would wipe out the flat 10-cent school fare and establish an escalator tying the school fare to the present and future adult fare has been introduced in the D.C. City Council by Hilda Mason (Statehood At Large) and three other council members, including Chairman Arrington L. Dixon (D) and Jerry A. Moore Jr. (R-At Large), chairman of the council's transportation committee. Mason and Moore, also members of the Metro board, have long advocated low transit fares.

Under the legislation, which has the general support of Mayor Marion Barry, the school fare would always be one-third of the lowest regular adult fare, rounded downward to the nearest nickel.

Public hearings on the higher fare formula have been scheduled for May 13 and 14 by the council's transportation committee. Given the District's time-consuming procedural rules, it is unlikely the new fare could go into effect before schools open in September.

The clampdown on the use of school fares on weekends and during vacation periods has been proposed by the city's transportation department, which announced last week that it plans to put the new rules into effect before schools close for the summer.

Under the proposed new rules, only pupils who are certified as attending classes during those periods would be permitted to buy special tickets valid at those times. The regular metal tokens used by pupils on school days would not be accepted. The restriction would save the city an estimated $600,000 a year in subsidy payments.