A major study of the nation's pension systems, from Social Security to Individual Retirement Accounts and the tax-deferred worker savings plan known as the 401(k), is under way in the House Ways and Means Committee.

Nobody had trouble determining the problem, said Reps. J.J. (Jake) Pickle (D-Tex.) and James R. Jones (D-Okla.) as they convened hearings last week. Finding the solution may prove more elusive.

The problem is that, at any given time, nearly half of the nation's workers are not in jobs covered by pension systems and are not accruing credits that would help to supplement Social Security benefits when they retire.

Most of the larger, more affluent firms have pension systems. Most uncovered workers, as noted in statistical analyses presented by Dallas Salisbury of the Employee Benefit Research Institute and Frank S. Swain of the Small Business Administration, are low- and middle-income workers for small businesses that often feel they cannot afford to establish pension systems.

Some such workers will eventually take jobs in which they are covered. But experts say that a large majority of those uncovered will stay that way, or not be covered long enough to build up a good pension. Most will have to depend on Social Security, designed to provide only one-third to one-half the amount needed to live on.

Salisbury's figures showed that, in 1983, only 49.5 million of 88.2 million nonfarm workers were in jobs with pension coverage. Two-thirds of those not covered were in jobs paying less than $15,000 a year.

While the proportion of under-$15,000 workers with coverage was about two-fifths, for higher-income workers, it was 70 percent or higher.

"In 1983, only 19 percent of workers in firms employing one to 24 workers were offered pension coverage, as compared to 41 percent in firms with 25 to 99 employes and 64 percent in businesses with 100 to 499 employes," Swain said. In firms with over 2,500, the figure was 96 percent in 1977, he said.

That is why private pensions in 1982 were going to only one-third of all married couples and one-sixth of unmarried persons 65 and over. It is also why private pensions provided the elderly only 7 percent of their income, compared with 40 percent from Social Security, 19 percent from earnings and 22 percent from assets income.

Private pensions are expected to provide more income, but experts agree that millions of retirees will not benefit.

Congress has created two major plans to allow workers to build a retirement nest egg through tax-free contributions. Businesses like this approach, since the worker foots at least part of the bill.

One is the IRA, which allows every worker to put aside $2,000 a year tax-free, or $2,250 if the worker's spouse is unemployed. The other is the 401(k), under which workers put part of their salary into a tax-free company savings plan through weekly payroll deductions that are usually matched by the employer.

The problem with these plans, as organized-labor representatives argued last week, is that they are used most by higher-income workers who need them least.

Low-income worker participation rates in 401(k) plans was far higher than in IRAs. Moreover, business spokesmen argued that continuing 401(k) plans, which the administration proposes to eliminate in its tax plan, is probably the best way to protect workers at small firms.