1. Muammo: Qotishmaning 60% misdan iborat va mis qo’rg’oshindan 2 kg ko’p. Qotishmada qancha mis bor? Formulalar: Mis miqdori = 0.6 * umumiy massa Qo’rg’oshin miqdori = umumiy massa - mis miqdori Mis qo’rg’oshindan 2 kg ko’p, ya’ni: $$\text{Mis} = \text{Qo’rg’oshin} + 2$$ Umumiy massa $M$ bo’lsa: $$0.6M = 0.4M + 2$$ $$0.6M - 0.4M = 2$$ $$0.2M = 2$$ $$M = 10$$ Mis miqdori: $$0.6 \times 10 = 6$$ Javob: 6 kg (C) 2. Muammo: Ikki quyma bor, qaysi birida qo’rg’oshin foizi ko’p? 1-quyma: 3 kg qo’rg’oshin, 2 kg mis Umumiy massa = 3 + 2 = 5 kg Qo’rg’oshin foizi: $$\frac{3}{5} \times 100 = 60\%$$ 2-quyma: 13 kg qo’rg’oshin, 7 kg mis Umumiy massa = 13 + 7 = 20 kg Qo’rg’oshin foizi: $$\frac{13}{20} \times 100 = 65\%$$ Javob: 2-quymaida 65% (B) 3. Muammo: Ikki quyma bor, qaysi birida qo’rg’oshin foizi ko’p? 1-quyma: 2 kg qo’rg’oshin, 6 kg mis Umumiy massa = 8 kg Qo’rg’oshin foizi: $$\frac{2}{8} \times 100 = 25\%$$ 2-quyma: 12 kg qo’rg’oshin, 3 kg mis Umumiy massa = 15 kg Qo’rg’oshin foizi: $$\frac{12}{15} \times 100 = 80\%$$ Javob: 2-quyma da 80% (C) 4. Muammo: 400 g 8% eritma va 600 g 13% eritma aralashmasining konsentrasiyasi? Umumiy massa: $$400 + 600 = 1000 \text{ g}$$ Mis miqdori: $$400 \times 0.08 + 600 \times 0.13 = 32 + 78 = 110 \text{ g}$$ Konsentratsiya: $$\frac{110}{1000} \times 100 = 11\%$$ Javob: 11% (A) 5. Muammo: 1 t mevaning 82% suv, keyin suv 70% ga tushdi. Yangi og’irlik? Dastlab suv miqdori: $$1000 \times 0.82 = 820 \text{ kg}$$ Qolgan qattiq qism: $$1000 - 820 = 180 \text{ kg}$$ Endi suv 70% bo’lsa, qattiq qism 30%: $$\text{Yangi massa} = \frac{180}{0.3} = 600 \text{ kg}$$ Javob: 600 kg (E) 6. Muammo: 2% yog’li 801 l sut bilan 5% yog’li sut aralashtirilsa, 3% yog’li sut olish uchun necha litr kerak? Formulalar: $$\text{(2%)} \times 801 + \text{(5%)} \times x = 3% \times (801 + x)$$ Hisoblash: $$0.02 \times 801 + 0.05x = 0.03(801 + x)$$ $$16.02 + 0.05x = 24.03 + 0.03x$$ $$0.05x - 0.03x = 24.03 - 16.02$$ $$0.02x = 8.01$$ $$x = \frac{8.01}{0.02} = 400.5$$ Javob: 400.5 litr (yaqin variant 40) (C) 7. Muammo: 140 g suvga 60 g tuz qo’shildi. Tuz foizi? Umumiy massa: $$140 + 60 = 200 \text{ g}$$ Tuz foizi: $$\frac{60}{200} \times 100 = 30\%$$ Javob: 30% (B) 8. Muammo: 40% va 35% eritmalar aralashtirilib, 37% eritma olish uchun har biridan necha litr kerak? Formulalar: $$0.4x + 0.35y = 0.37(x + y)$$ Faraz qilaylik $x + y = 1$ litr, shunda: $$0.4x + 0.35(1 - x) = 0.37$$ $$0.4x + 0.35 - 0.35x = 0.37$$ $$0.05x = 0.02$$ $$x = 0.4$$ Shunday qilib: $$y = 1 - 0.4 = 0.6$$ Javob: 0.4 va 0.6 litr (C)