Perturbed members of the House Ways and Means Committee peppered representatives of the Reagan administration yesterday with a simple question: Why does the government want to sell Conrail when the transaction apparently would lose money for the government?

Officials from the Treasury and Transportation departments denied that the sale of the railroad, proposed by Transportation Secretary Elizabeth Hanford Dole last March, is a loser. They said terminating other Conrail-related costs to the government would offset the fact that the revenue-losing tax benefits to the purchaser, Norfolk Southern Corp., seem to be greater than the purchase price of $1.2 billion.

Ways and Means, as well as the House Energy and Commerce Committee, must approve the sale. Questions from the relatively few members present made it appear that approval could be hard to win.

"What I'm interested in is whether we're selling an asset that earns money for the United States, at zero cost," said Rep. Byron L. Dorgan (D-N.D.).

Committee Chairman Dan Rostenkowski (D-Ill.) said the committee would be wary about approving the sale until the administration submitted "more definite numbers."

Rep. James J. Florio (D-N.J.), chairman of the Energy and Commerce subcommittee that has jurisdiction over Conrail, told the committee "the effect of the transaction is that taxpayers will be paying to give away the railroad."

Federal Railroad Administrator John H. Riley replied that, although the government couldn't provide hard figures of the revenue effect of the sale, "of all the options the government has, including keeping it, this is the highest net." He pointed out that Conrail, the quasi-government entity formed from the bankrupt Penn Central in 1976, lost money for years until it finally turned a profit in 1983.

Norfolk Southern has agreed to give up two significant tax breaks, use of the investment tax credit and a provision that permits operating losses to be applied years after they occur. Those both would have been available to it if this were a private purchase.

But it will be able to depreciate -- write off over a period of years -- Conrail's assets to the tune of $3.1 billion. However, Treasury official Dennis Ross said the administration would accept limiting that depreciation basis to the actual value of the property if it turns out to be smaller than the tax basis.