Peoples Drug Stores Inc.'s second-quarter profits jumped 52 percent to a record $1.78 million (35 cents a share) from $1.17 (23 cents) last year, Washington's biggest drug store chain reported yesterday.

Sales at the 566 Peoples stores climbed to $174.6 million for the quarter, up 15 percent from $151.3 million in the same period a year ago. For the first half of the fiscal year, sales totaled $423.4 million, compared with $366.8 million in the first six months of 1982.

Some of the sales growth came from opening additional stores, but President Sheldon W. Fantle said sales for the stores that existed a year ago were up 12 percent for the quarter.

First-half earnings for the chain were up 24 percent to $6.98 million from $5.65 million. Fantle said the sales gains plus a reduction in interest expense were responsible for the boost in profits.

Record profits also were reported by Family Entertainment Centers Inc., the operator of Chuck E. Cheese's Pizza Time Theatre restaurants in the Middle Atlantic States.

The Rockville firm earned $274,000 (16 cents a share) on sales of $5.3 million in its first quarter ended April 3 compared with a loss of $51,000 (4 cents) on sales of $1.49 million in the first quarter of 1982. The gains came primarily from opening new stores.