1. Problem: Express 6 : 25 as a percent. To convert a ratio to a percent, divide the first number by the second and multiply by 100. $$\frac{6}{25} \times 100 = 24\%$$ 2. Problem: Express 75 % as a ratio and decimal. (a) Ratio: 75 % means 75 per 100, which simplifies to $$\frac{3}{4}$$ or 3:4. (b) Decimal: 75 % as decimal is $$0.75$$. 3. Problem: Find 46 % of 650. Calculate $$\frac{46}{100} \times 650 = 299$$. 4. Problem: Ravi's attendance is 85 % of 220 days. Find absent days. Present days = $$0.85 \times 220 = 187$$. Absent days = $$220 - 187 = 33$$. 5. Problem: A's salary is 50 % higher than B's. Find by what percent B's salary is lower than A's. Let B's salary = 100. A's salary = 100 + 50 = 150. Percent decrease from A to B = $$\frac{150 - 100}{150} \times 100 = 33.33\%$$. 6. Problem: Arun's income is 9600, expenditure is 60 %. Find savings. Expenditure = $$0.60 \times 9600 = 5760$$. Savings = $$9600 - 5760 = 3840$$. 7. Problem: Mr. Gulati has 96400. He gave 42 % to wife, 35 % to son, rest to daughter. Wife's share = $$0.42 \times 96400 = 40488$$. Son's share = $$0.35 \times 96400 = 33740$$. Daughter's share = $$96400 - (40488 + 33740) = 22172$$. 8. Problem: Population 103500, 56 % male. Find females. Males = $$0.56 \times 103500 = 57960$$. Females = $$103500 - 57960 = 45540$$. 9. Problem: A man loses 25 % money, then spends 20 % of rest, left with 10200. Find original money. Let original money = $$x$$. After 25 % loss, money left = $$0.75x$$. After spending 20 % of rest, money left = $$0.80 \times 0.75x = 0.6x$$. Given $$0.6x = 10200$$, so $$x = \frac{10200}{0.6} = 17000$$. 10. Problem: Find $$x$$ if (i) 2.25 % of $$x$$ is 630, (ii) 35 % of $$x$$ is 525. (i) $$0.0225x = 630 \Rightarrow x = \frac{630}{0.0225} = 28000$$. (ii) $$0.35x = 525 \Rightarrow x = \frac{525}{0.35} = 1500$$. 11. Problem: Find (i) 24 % of 650, (ii) 85 % of 400, (iii) 125 % of 80. (i) $$0.24 \times 650 = 156$$. (ii) $$0.85 \times 400 = 340$$. (iii) $$1.25 \times 80 = 100$$. 12. Problem: Asha deposits 1200 which is 20 % of income. Find income. Let income = $$x$$. $$0.20x = 1200 \Rightarrow x = \frac{1200}{0.20} = 6000$$. 13. Problem: Population increases from 160000 to 180000. Find percentage increase. Increase = $$180000 - 160000 = 20000$$. Percentage increase = $$\frac{20000}{160000} \times 100 = 12.5\%$$. 14. Problem: Book price 2100, rebate 15 %. Find rebate and net price. Rebate = $$0.15 \times 2100 = 315$$. Net price = $$2100 - 315 = 1785$$. 15. Problem: Aditya got 78 % marks = 663. Find maximum marks. Let max marks = $$x$$. $$0.78x = 663 \Rightarrow x = \frac{663}{0.78} = 850$$. 16. Problem: Shruti's marks: 60 % of 75, 55 % of 60, 60 % of 65. Find aggregate percentage. Marks obtained = $$0.60 \times 75 + 0.55 \times 60 + 0.60 \times 65 = 45 + 33 + 39 = 117$$. Total max marks = $$75 + 60 + 65 = 200$$. Aggregate percentage = $$\frac{117}{200} \times 100 = 58.5\%$$. 17. Problem: Divide 1560 among A, B, C such that A = 50 % of B, B = 20 % of C. Let C = $$x$$. Then B = $$0.20x$$, A = $$0.50 \times 0.20x = 0.10x$$. Total = $$A + B + C = 0.10x + 0.20x + x = 1.30x = 1560$$. $$x = \frac{1560}{1.30} = 1200$$. So, C = 1200, B = $$0.20 \times 1200 = 240$$, A = $$0.10 \times 1200 = 120$$. Final answers: 1. 24 % 2. (a) 3:4, (b) 0.75 3. 299 4. 33 days 5. 33.33 % 6. 3840 7. Wife: 40488, Son: 33740, Daughter: 22172 8. 45540 females 9. 17000 10. (i) 28000, (ii) 1500 11. (i) 156, (ii) 340, (iii) 100 12. 6000 13. 12.5 % 14. Rebate: 315, Net price: 1785 15. 850 16. 58.5 % 17. A: 120, B: 240, C: 1200