170. During spring, Zhenya lost $20 \%$ of his weight, then gained $30 \%$ during summer, lost $20 \%$ again during autumn, and gained $10 \%$ during winter. Did Zhenya gain or lose weight over the year?
Solution. Let's assume Zhenya's mass was 100 (units of mass). Then after spring, his mass became $100-20=80$ (units of mass), after summer $-80+\frac{30 \cdot 80}{100}=104$ (units of mass), after autumn $-104-$ $-\frac{20 \cdot 104}{100}=104-20.8=83.2$ (units of mass). After winter, Zhenya's mass became $83.2+8.32=91.52$ (units of mass).

Answer: Zhenya lost weight.