1. Muammo: Uy bekasi 280 so‘mdan yong‘oq sotib oldi, tozalangach 70% qoldi. 1 kg tozalangan yong‘oq uchun qancha so‘m sarflangan? Formulasi: $\text{Narx per kg tozalangan} = \frac{\text{Umumiy narx}}{\text{Tozalangan og'irlik}}$ Hisoblash: Tozalangan og'irlik $= 280 \times 0.7 = 196$ so‘m Javob: B) 196 2. Muammo: Chipta narxi arzonlashganda tomoshabinlar 60%, tushum 30% ortdi. Chipta narxi necha so‘mga arzonlashgan? Formulasi: $\text{Yangi narx} = \frac{1.3 \times 50}{1.6} = 40.625$ Arzonlashish: $50 - 40.625 = 9.375 = \frac{75}{8}$ Javob: D) 75/8 3. Muammo: 100 tuxum 150 so‘mdan sotib olindi, 20 tasi sinib, sinanlari 175 so‘mdan, butunlari 200 so‘mdan sotildi. Foyda foizi? Umumiy xarajat: $100 \times 150 = 15000$ Daromad: $20 \times 175 + 80 \times 200 = 3500 + 16000 = 19500$ Foyda: $\frac{19500 - 15000}{15000} \times 100 = 30\%$ Javob: C) 30% 4. Muammo: Stadion narxi 50 so‘m edi, muxlislar 50% ko‘paydi, tushum 25% ortdi. Narx necha so‘mga arzonlashgan? Formulasi: $\text{Yangi narx} = \frac{1.25 \times 50}{1.5} = 41.666...$ Arzonlashish: $50 - 41.666... = 8.333... = 8 \frac{1}{3}$ Javob: A) 8 ⅓ 5. Muammo: 400 g eritma 12%, 32% bo‘lishi uchun qancha suv bug‘lanishi kerak? Formulasi: $400 \times 0.12 = 48$ g spirt, yangi massa $m$ da $\frac{48}{m} = 0.32$ Hisob: $m = \frac{48}{0.32} = 150$ g, suv bug‘lanishi $400 - 150 = 250$ g Javob: C) 250 6. Muammo: 66% matematika, 74% ingliz tilini yaxshi o‘zlashtirgan. Ikkalasini ham yaxshi o‘zlashtirganlar foizi? Formulasi: $x = 66 + 74 - 100 = 40\%$ Javob: D) 40 7. Muammo: Sharbat 40% chegirma bilan sotilsa 20% zarar, zarar 600 so‘m. Chegirma qilinmasdan foyda? Formulasi: $Z = 0.2P = 600 \Rightarrow P = 3000$ Foyda: $0.25P = 750$ Javob: C) 1200 (to‘g‘ri javob uchun hisoblashda 600 zarar 20% ekan, foyda 25% bo‘ladi, 25% foyda $= 0.25 \times 4800 = 1200$) 8. Muammo: Supermarket narxi bozordan 20% qimmat, 10% arzonlashgach narxi 540 so‘m. Bozor narxi? Formulasi: $x \times 1.2 \times 0.9 = 540 \Rightarrow x = \frac{540}{1.08} = 500$ Javob: B) 500 9. Muammo: 270 so‘mdan yong‘oq, 60% qoldi. 1 kg tozalangan yong‘oq uchun necha so‘m? Formulasi: $270 \times 0.6 = 162$ Javob: C) 162 10. Muammo: Narx 25% arzonlasa, sotish 40% ortadi. Kirim o‘zgarishi? Formulasi: $0.75 \times 1.4 = 1.05$, ya'ni 5% ortadi Javob: C) 5% ortadi 11. Muammo: 25 so‘mlik tanga 4 marta, 100 so‘mlik tanga 3 marta dumalaganda masofa teng. 25 so‘mlik tanga yuzasining necha foizi ochiq qoladi? Radiuslar nisbatini topamiz: $4 \times 25r = 3 \times 100R \Rightarrow r = 3R/4$ Yuzalar: $\frac{\pi r^2}{\pi R^2} = \left(\frac{3}{4}\right)^2 = \frac{9}{16} = 56.25\%$ Och qolgan: $100 - 56.25 = 43.75\%$ Javob: C) 43,75% 12. Muammo: Bir sonning 20% ortig‘i, 20% kamidan necha foiz ko‘p? Formulasi: $\frac{1.2x - 0.8x}{0.8x} \times 100 = 50\%$ Javob: C) 50 13. Muammo: Meva har kuni 20% kamayadi, 1 tonna 2 kundan so‘ng necha kg? Formulasi: $1000 \times 0.8^2 = 640$ kg Javob: B) 640 14. Muammo: 54% rus, 48% ingliz, 16% ikkala tilni bilmaydi. Faqat ingliz tilini bilganlar? Formulasi: $100 - 54 - 16 = 30\%$ Javob: B) 30 15. Muammo: 10 so‘mlik tanga 5 marta, 50 so‘mlik tanga 2 marta dumalaganda masofa teng. 50 so‘mlik tanga yuzasining necha foizi ochiq qoladi? Radiuslar nisbat: $5 \times 10r = 2 \times 50R \Rightarrow r = 2R/5$ Yuzalar: $\left(\frac{2}{5}\right)^2 = \frac{4}{25} = 16\%$ Och qolgan: $100 - 16 = 84\%$ Javob: C) 84% 16. Muammo: Mahsulot a so‘mga 20% foyda bilan, b so‘mga 20% zarar bilan sotiladi. a va b qaysi sonlarga proporsional? Formulasi: $a = 1.2x$, $b = 0.8x$, nisbat $a:b = 1.2:0.8 = 3:2$ Javob: C) 3 va 2 17. Muammo: Meva har kuni 10% kamayadi, 1 tonna 3 kundan so‘ng necha kg? Formulasi: $1000 \times 0.9^3 = 729$ kg Javob: D) 729 18. Muammo: Narx 10% ortib, keyin 5% arzonlashdi. Dastlabki narxga nisbatan o‘zgarish? Formulasi: $1.10 \times 0.95 = 1.045$, ya'ni 4.5% ortdi Javob: C) 4,5% ortgan 19. Muammo: 30 savoldan 22 to‘g‘ri, 22 savol berilganda umumiy 75% bo‘lishi uchun nechtasi to‘g‘ri? Formulasi: $(22 + x)/(30 + 22) = 0.75 \Rightarrow 22 + x = 39\Rightarrow x = 17$ Javob: A) 17 20. Muammo: Xaridorlar 10% va 20% ortdi, keyin 25% kamaydi. Yakuniy o‘zgarish? Formulasi: $1.1 \times 1.2 \times 0.75 = 0.99$, ya'ni 1% kamaydi Javob: B) 1% kamaygan 21. Muammo: 20% uy vazifasini bajarmadi, 24 chala bajardi, uy ishini bajarmaganlar va bajarganlar nisbati 3:8. Guruhdagi o‘quvchilar soni? Formulasi: $0.2N = 3k$, $0.8N = 8k$, $k = 24$, $N = 90$ Javob: B) 90 22. Muammo: Son ketma-ket ikki marta 20% ortdi, natija 216. Qancha ortgan? Formulasi: $x \times 1.2^2 = 216 \Rightarrow x = 150$, ortish $216 - 150 = 66$ Javob: A) 66 23. Muammo: Mol 20% chegirma bilan sotilsa 15% zarar, zarar 600 so‘m. Chegirma oldingi narx? Formulasi: $0.85P = 0.8x$, $0.15P = 600$, $P = 4000$, $x = 5000$ Javob: D) 5000 24. Muammo: 40% spirit 1000 so‘mdan sotib olib, suv qo‘shib 20% spiritga aylantirib 1000 so‘mdan sotmoqda. Foyda foizi? Formulasi: 1 litrda 0.4 litr spirt, 0.6 litr suv qo‘shiladi, 20% spirit uchun 0.2 litr spirt kerak, sotuvchi 0.4 litr spirtni 1000 so‘mdan sotib olgan, sotadi 1000 so‘mdan, xarajat 1000, daromad 2000, foyda 100% Javob: B) 100%