The Metro Board will begin hearings throughout the Washington area next week on fare increases for both the bus and subway systems. The raises would take effect June 29.

The hearings in Maryland, both of which will begin at 7:30 p.m., are scheduled as follows:

March 31 -- Largo Senior High School, 505 Largo Rd., Upper Marlboro.

April 3 -- Montgomery County Office Building, 100 Maryland Ave., Rockville.

Metro is projecting a record $276 million operating budget for the fiscal year beginning July 1, a 44 percent increase over the preceding year. Although some of that increase represents the cost of extending the subway's Blue Line to Capitol Heights and Addison Road late this year, much of it is a result of inflation. Diesel Fuel prices, for example, have more than doubled during the past year.

The proposed fare increases, combined with new passes and increased parking lot fees, are expected to raise between $8.5 million and $12.4 million in added revenue. Maryland's projected share of the Metro deficit is $21.8 million. Metro has adopted a general guideline in recent years of annual fare increases to keep pace with inflation. Subway Fares

Two subway fare schedules are up for discussion. One would raise rush-hour fares approximately 11 percent for all trips; the other would raise rush-hour fares approximately 22 percent for all trips. Rush hour fares are charged weekdays between 6 and 9:30 a.m. and between 3 and 6:30 p.m.

Under the 11 percent solution, the basic rush-hour fare would increase from 45 cents to 50 cents for a three-mile trip. An additional 10.5 cents would be charged for each additional mile.

A trip from Silver Spring to Metro Center, now costing 90 cents, would go up to $1. A ride from New Carrollton to Metro Center would go from $1.15 to $1.25.

Under the 22 percent plan, the minimum rush-hour fare for a three-mile trip would be 55 cents, and 11.5 cents would be charged for each additional mile. The fare from Silver Spring to Metro Center would go from 90 cents to $1.10; the trip from New Carrollton to Metro Center would increase from $1.15 to $1.40.

There would be no charge in the present 50-cent off-peak fare for all trips regardless of length that is charged at midday, at night and on weekends and holidays.

Fares for elderly and handicapped persons would continue at one-half the price of the rush-hour fare, to a maximum of 50 cents per trip. Bus Fares

The basic rush-hour Maryland bus fare would be increased from 55 to 60 cents. The zone charge between D.C. and Maryland would jump from 35 cents to 40 cents. Rush-hour fares between Maryland and D.C. are indicated in the accompanying chart.

The off-peak bus fare would be raised from 40 cents to 45 cents, and the zone charge between D.C. and Maryland would jump from 20 cents to 25 cents.

The 25-cent surcharge on bus routes N-7 and N-9 would be retained.

Bus fares for the elderly and handicapped would be increased to one-half the rush-hour fare at all times. The present policy is to charge one-half the off-peak fare at all times. Rail-Bus Transfers

Transfers from bus to subway will continue to be forbidden.

Riders can transfer free from subway to bus within the District of Columbia.

At Maryland stations, the rail-to-bus transfer price would increase from 10 cents to 15 cents at all times, plus zone charges.

The accompanying charts list sample round-trip, combined bus and subway fares from points in Maryland to Metro Center downtown. Passes

Maryland jurisdictions are proposing four possible passes, all of which would be valid for two-week periods:

A $10 pass good for unlimited bus trips within Maryland and $4 of rail trips anywhere.

A $12 pass good for unlimited bus trips within Maryland and $6 of rail trips anywhere.

A $16 pass good for unlimited bus trips between or within D.C. or Maryland and $4 of rail trips anywhere.

An $18 pass good for unlimited bus trips between or within D.C. or Maryland and $6 of rail trips anywhere. Parking Lots

Parking fees at all Metro-operated lots would be increased 25 cents. That means it would cost $1 at New Carrollton and $1.25 everywhere else Metro has a lot.