Percentages

The problem states: 20% of 40 + ?% of 80 = 120. First, calculate 20% of 40, which is (20/100)*40 = 8. Let the unknown percentage be x%. Then the equation becomes 8 + (x/100)*80 = 120. Simplifying, (x/100)*80 = 120 - 8 = 112. This gives 0.8x = 112, so x = 112 / 0.8 = 140. Therefore, the value of '?' is 140%, which corresponds to option A. The original answer given as D (180) is incorrect. The options represent the percentage values directly, so the correct answer is A (140).

Calculate 32% of 425: 0.32 × 425 = 136. The equation is 136 - (x% of 250) = 36. Rearranging gives x% of 250 = 136 - 36 = 100. So, (x/100) × 250 = 100, which means x = (100 × 100) / 250 = 40%. Therefore, the value of '?' is 40, which corresponds to option B.

Let x be the unknown percentage. The equation is x% of 400 + 40% of 160 = 17% of 400. Converting percentages to decimals and multiplying: (x/100)*400 + 0.4*160 = 0.17*400. This simplifies to 4x + 64 = 68. Solving for x gives 4x = 4, so x = 1. Therefore, the correct value of x is 1%, which corresponds to option C.

To find the unknown number, convert percentages to decimals and set up the equation: 0.1666 * 0.3333 * 0.6666 * x = 30. Multiplying the decimals gives approximately 0.037, so x ≈ 30 / 0.037 ≈ 810, which matches option C.

To find 43% of 784, multiply 784 by 0.43: 784 × 0.43 = 337.12. This matches option C. Therefore, the correct answer is C, not B.

The equation simplifies to ((50 - x/29) × 4200%) = 3√196. Since 4200% = 42 and 3√196 = 3 × 14 = 42, the equation becomes (50 - x/29) × 42 = 42. Dividing both sides by 42 gives 50 - x/29 = 1. Solving for x gives x/29 = 49, so x = 49 × 29 = 1421. Therefore, the correct value of ? is 1421, which corresponds to option D.

First, calculate inside the parentheses: (27 + 3) = 30. Then, 33.33% of 30 is approximately 10. Next, divide by 5: 10 ÷ 5 = 2. Multiply by 21: 21 * 2 = 42. Subtract 7: 42 - 7 = 35. Then, take 3/7 of 35: (3/7) * 35 = 15. Finally, subtract 8: 15 - 8 = 7. Thus, the answer is 7, which corresponds to option A.

Calculating 15% of 195 gives 0.15 × 195 = 29.25. Calculating 14% of 205 gives 0.14 × 205 = 28.7. Adding these two results gives 29.25 + 28.7 = 57.95, which rounds to 58. Therefore, the correct answer is option C (58). The original correct answer B (62) was incorrect, and the explanation correctly identified the right answer as 58.

Calculating 26.98% of 6002 gives approximately 1618.7, and 45.01% of 4199 gives approximately 1889.6. Adding these results in about 3508.3, which rounds to 3500, matching option B.

Given the equation x% of 80 equals 20% of y, we write it as (x/100)*80 = (20/100)*y. Simplifying, 0.8x = 0.2y, which leads to y = 4x. If we take x = 20, then y = 4*20 = 80. Therefore, the correct values are x = 20 and y = 80, which corresponds to option C.

To solve (332% of 2113) / 42, first convert 332% to decimal form: 332% = 3.32. Then multiply 3.32 by 2113 to get 7015.16. Next, divide 7015.16 by 42, which equals approximately 167.03. Among the options, 167 (A) is the closest and correct answer.

Let the capacity of container A be x liters. Container B has 62.5% less than A, so B = x - 0.625x = 0.375x liters. Since all water from A is poured into B and C, C = x - 0.375x = 0.625x liters. After transferring 148 liters from C to B, both have equal amounts: 0.375x + 148 = 0.625x - 148. Solving gives x = 888 liters.

The amount increases by 1/8th each year, so after one year it becomes 64000 + (1/8)*64000 = 64000 * 9/8 = 72000. After the second year, it increases by 1/8th again: 72000 * 9/8 = 81000. Hence, the amount after two years is Rs.81000.

After a 10% increase, the population becomes 1.1 times the original. Then a 10% decrease makes it 0.9 times the increased population, so overall it is 1.1 × 0.9 = 0.99 times the original. Given the final population is 7920, the original population = 7920 ÷ 0.99 = 8000. However, this calculation shows 8000, so the correct answer should be B, not D. Rechecking: 8000 × 1.1 = 8800; 8800 × 0.9 = 7920. So the original population is 8000, option B is correct.

The population increases by 4% per annum plus an additional 1% per annum due to job seekers. These increases compound multiplicatively each year, so the effective annual growth rate is (1 + 0.04) × (1 + 0.01) - 1 = 1.04 × 1.01 - 1 = 0.0504 or 5.04% per year. Over 2 years, the total increase is (1.0504)^2 - 1 = 1.103 - 1 = 0.103 or 10.3%. Among the given options, 10.25% (option C) is the closest to the correct value of 10.3%. Therefore, option C is the correct answer, not option D.

At 50 kmph, mileage is 20 km/l. At 70 kmph, mileage decreases by 10%, so new mileage = 20 - 10% of 20 = 18 km/l. With 12 liters, distance = 18 × 12 = 216 km, which corresponds to option A.

Let the third number be x. The first number is 20% more than x, which is 1.2x. The second number is 50% more than x, which is 1.5x. The ratio of the two numbers is therefore 1.2x : 1.5x = 1.2 : 1.5 = 12 : 15 = 4 : 5. Hence, the correct ratio is 4 : 5, which corresponds to option C.

The original ratio of seats is 5:8. Increasing 5 by 30% gives 5 × 1.3 = 6.5, and increasing 8 by 25% gives 8 × 1.25 = 10. The new ratio is 6.5:10, which simplifies to 13:20.

Given that 96% of the population is 23040, the total population can be found by dividing 23040 by 0.96. This calculation is 23040 ÷ 0.96 = 24000. Therefore, the total population of the village is 24000, which corresponds to option B.

The original ratio of boys to girls is 7:8. After a 20% increase in boys, the number becomes 7 × 1.20 = 8.4. After a 10% increase in girls, the number becomes 8 × 1.10 = 8.8. The new ratio is 8.4 : 8.8, which simplifies to 21 : 22 when multiplied by 5, but since the options do not include 21:22 as the correct ratio, let's check the options carefully. Actually, 8.4 : 8.8 simplifies to 21 : 22, which matches option C. Therefore, option C is correct, not B. The initial correction was incorrect. The new ratio is 21:22, so option C is correct.

60% of 50 is 0.6 × 50 = 30, and 40% of 30 is 0.4 × 30 = 12. The difference is 30 - 12 = 18, so 60% of 50 is 18 greater than 40% of 30.

To find 25% of 30% of 45%, convert percentages to decimals and multiply: 0.25 × 0.30 × 0.45 = 0.03375.

Let the number be x. 60% of x is 0.6x. According to the problem, 0.6x - 40 = 50. Adding 40 to both sides gives 0.6x = 90. Dividing both sides by 0.6 gives x = 150. However, 150 is option A, so we need to re-check the calculation. Actually, 0.6x - 40 = 50 implies 0.6x = 90, so x = 90 / 0.6 = 150. Therefore, the correct answer is A, not B. The initial correction was incorrect. The correct answer is A (150).

Let the first number be x and the second number be y. Given 40% of x equals two-thirds of y, so 0.4x = (2/3)y. Rearranging, x/y = (2/3) / 0.4 = (2/3) / (2/5) = (2/3) * (5/2) = 5/3. Thus, the ratio of the first number to the second number is 5:3.

Given that x is 20% more than z, we have x = 1.20z. Similarly, y is 80% more than z, so y = 1.80z. The ratio x:y = 1.20z : 1.80z = 1.20 : 1.80. Simplifying this ratio by dividing both terms by 0.60 gives 2 : 3. Therefore, the correct ratio x:y is 2:3, which corresponds to option D.