The average age of the 40 people seated in a hall is 32 years. The 10 people in the front row are on average 4 years younger than the 30 people behind them. What is the average age of the front row?

Let the front row average $f$ years, so the 30 behind average $f+4$. Then $10f+30(f+4)=40\times 32=1280$, that is $40f+120=1280$, so $f=29$ (and the rows behind average 33). Check: $10\times 29+30\times 33=290+990=1280$. 30 takes half the 4-year gap off 32, which would be right only if the two groups were the same size; the larger group pulls the overall average towards itself, so the small front row must sit further below 32 than half the gap. 28 takes the whole 4 years off. 33 is the average of the 30 seated behind, not of the front row.