QUESTION: Could someone explain what a single supplement buys? For example, last year on a Perillo tour to Italy, the supplement was $399.

ANSWER: All the single supplement buys is privacy.

The cost that is cited for tour packages is almost always based on two people sharing a room (or ship cabin), and those who occupy a room alone often are charged extra.

A spokeswoman for Perillo Tours said their single supplement is "not our charge, it's the hotel's charge." (For your tour this year, the supplement is $539.)

Hotels almost always negotiate with tour operators on the basis of double occupancy; it is more profitable to take in $100, say, for two in a room than $75 for one.

Also, two people eat and drink more at a hotel than one, and the hotel wants to make up for what it sees as lost revenues. So the tour agency levies a supplement to make up for what it loses on the room if one person occupies it.

According to Paula Saint-Amour, senior vice president for wholesale travel for American Express, the single supplement is practically universal in Europe, but is not always charged for some newer domestic hotels and resorts, which take into account the fact that a certain portion of single travelers will be staying there.

There are no single supplements for American Express's independent packages in Hawaii, where there are many new hotels, she said, though there is still a supplement for escorted tours there.

If your privacy is not worth the extra charge, one option is to ask a tour company if it will provide another willing single traveler as a roommate. Both Perillo and American Express will do that.

Another option is to use a service that matches singles who want a travel companion, either through newletters with ads or by putting putting people in touch. The services generally charge a fee.

Among them: Travel Companion Exchange, Post Office Box 833, Amityville, N.Y. 11701; (516) 454-0880. Partners in Travel, Post Office Box 491145, Los Angeles, Calif. 90049; (213) 476-4869. Travel in Twos, 239 North Broadway, Suite 3, North Tarrytown, N.Y. 10591; (914) 631-8409. Odyssey Network, 118 Cedar Street, Wellesley, Mass. 02181; (617) 237-2400.

QUESTION: I would appreciate any information on organized trips on the Colorado through the Grand Canyon.

ANSWER: Here are some of the companies that offer trips through the Grand Canyon; many run trips on other parts of the Colorado and on other rivers. Participants taking a segment of the canyon usually have to hike 9 or 10 miles in or out. The prices include all equipment, including camping gear, and meals and may include transportation to and from the river.

Sobek's Whitewater, Post Box 1359, Angels Camp, Calif. 95222; (800) 888-0229. An eight-day motorized raft trip, from Lees Ferry to Lake Mead is $1,195.

Dvorak Kayak and Rafting Expeditions, 17921 Highway 285, Nathrop, Colo. 81236; (800) 824-3795 or (719) 539-6851. Six-day upper-canyon rafting trips are $581, 8 days is $851 and 12 days is $1,732.

Wilderness River Adventures, Post Office Box 717, Page, Ariz. 86040; (800)TH992-8022. A three-and-a-half-day motorized upper canyon trip is $473. Motorized trips of 7 days are $1,117, 8 days are $1,260 and a 12-day oar trip is $1,544.

High Desert Adventures, 240 East Morris Avenue, Salt Lake City, Utah 8411; (800) 345-7238. Five-day oar-powered trips are $851; 8 days, $1,292, and 12 days at $1,732. A motorized raft trip of 8 days is $1,495.

OARS, Post Office Box 67, Angels Camp, Calif. 95222; (800) 346-6277 or (800) 446-7238. Oar-powered raft trips, 13 days, are $2,053. A six-day segment is $1,093 and nine days is $1,567. The company also runs trips on dories. The whole canyon, usually 16 days, is $2,410; the upper segment, six days, is $1,193 and the lower section, 11 days, $1,817. A five-day sampler includes a night at a dude ranch, helicopter into the canyon and a raft ($848) or dory ($825) trip.

Grand Canyon Expeditions, Post Office Box O, Kanab, Utah 84741; (800) 544-2691. An eight day-trip on a motorized raft is $1,495, and a 14-day rowing expedition in a dory with motor support is $1,895.

QUESTION: I hear that it is imperative to book early for the Galway Races in Ireland, yet no one seems to know when the races take place or how one gets tickets.

ANSWER: The Galway Races, at Ballybrit Race Track just outside Galway, will be July 29 to Aug. 3 this year. The Galway Plate, the premier steeplechase of the week, will be July 31 and the Galway Hurdle, another major race, will be Aug. 1.

General admission is $9 on July 29 and 30 and Aug. 2 and 3, and $13 on July 31 and Aug. 1. These tickets are always available at the gate. For an extra $4.60 racegoers may watch from an upper deck. There are also reserved seats for $22.25 a day.

QUESTION: I would like to see some of the principal sites of the western front of World War I. Are there organizations that could expedite such a trip?

ANSWER: One organization that focuses on European battlefields is Major & Mrs. Holt's Battlefield Tours, Golden Key Building, 15 Market Street, Sandwich, Kent CT13 9DA, England; telephone (304) 612248.

The three-day "It's a Long Way to Tipperary" tour is the most popular World War I itinerary, the company says. It follows the British Expeditionary Force route in France over Mont Cassel to Ypres in Belgium, and also visits the Vimy Ridge and Somme battlefields. The cost is $398 a person ($68 single supplement).

There are three-day tours focusing solely on the Somme or on Ypres, and one on winners of the Victoria Cross at the Somme, April 13 to 15, $402. A tour focusing on Operation Michael, the March 1918 German attack in France, takes place April 27 to 29, costs $402. An April 3 to 7 itinerary in France and Belgium is based on poems, songs, letters and diaries of various writers; the cost is $596. Prices generally include hotel, breakfast and dinner daily and transportation to and from London.

Another tour leader is Graham Maddocks, 10 Ashburton Avenue, Birkenhead, Merseyside LT43 8TJ, England;

653 7108. Mr. Maddocks will mark the 75th anniversary of the battles of the Somme, visiting the battlefields July 22 to 28. The price is $592 ($24 a night single supplement).- Information about tours such as these is also available from your travel agent.