The nation's economy grew somewhat more rapidly last quarter than previously estimated, the government reported yesterday, but inflation was substantially worse - providing a mixed bag for Carter administration policymakers.

Revised figures from the Commerce Department showed the "real" gross national product, or tctual volume of output, grew at an 8 per cent annual rate in the April-June period, rather than the 7.4 percent reported earlier.

At the same time, however, the GNP price index soared at a 10.7 percent annual rate, compared to a 10 percent pace estimated previously. The rise was the steepest since the final quarter of 1974.

Meanwhile, the department also reported a sharp jump in corporate profits, steemming in part from the overall second-quarter rebound. Profits after taxes rose by $15.2 billion, or 14.9 percent, following a first-quarter decline.

The revised figures on output constituted good news for the administration.Most analysts had expected the economy to grow at an 8 to 9 per cent pace, and the preliminary estimates had been a disappointment.

The administration hopes to see the economy grow by 4.1 per cent for the year as a whole, down from a 4.9 per cent rise in 1977. Yesterday's revisions in effect bolstered prospects for reaching that target.

Moreover, the stronger-than-estimated performance came in areas where the economy can use additional strength - business investment in new plant and equipment, and net exports.

At the same time, the revisions showed that inventory accumulation was less-robust than thought previously - easing some concerns that inventories may be piling up at an unhealthy pace.

The inflation figures were quite another story, however. The 10 per cent pace reported earlier had been considered bad enough. The revisions stemmed mainly from increased construction costs, but still were substantial.

Nevertheless, William A. Cox, a department economist, said the figures won't change the administration's forecast for the rest of this year. Cox predicted the inflation rate would abate visibly between now and December.

The figures no corporate profits contained one particularly heartening note: Profits from current production, which exclude inventory profits, rose a healthy $26.9 billion, or 20.3 per cent - a sharp gain by any measure.

Before-tax book profits rose $29.5 billion, or 17.1 per cent, but most of this reflected increases in inventory profits. Profits of domestic non-financial corporations rose $25.3 billion.

The revised second-quarter rise in output essentially marked a rebound from the cold weather and coal strike that depressed the economy in the first three months of this year.Real output declined during that period at an 0.1 per cent annual rate.