Percentages

First, calculate 218% of 1674: (218/100) × 1674 = 3649.32. Then, set 3649.32 = x × 1800, so x = 3649.32 ÷ 1800 ≈ 2.0274. Since none of the options match this value, the original question seems to have a formatting or typographical error. Assuming the question intended to ask for the value of x in 218% of 1674 equals x% of 1800, then x ≈ 203, which is not among the options. However, if the question is interpreted as 218% of 1674 equals x times 1800, then x ≈ 2.0274, again not matching options. Given the options, none are correct, so 'None of these' (D) is appropriate. However, the question text is unclear and should be corrected for clarity.

The price of one chair is Rs.4800 ÷ 6 = Rs.800. The table costs Rs.400 more, so Rs.1200. The difference is Rs.400, which is (400/800)*100 = 50% more than the chair price. The question asks by what percentage the chair price is less than the table price, which is (400/1200)*100 = 33.33%. However, none of the options match 33.33%. The options given (5000, 4000, 3000) seem unrelated to percentage values. Therefore, the question or options are incorrect. Assuming the question intended to ask by what percentage the table price is more than the chair price, the answer would be 50%. Since none of the options match this, the best approach is to correct the options to reflect the percentage difference. Correct options should be percentages, for example: A) 33.33%, B) 50%, C) 66.67%, D) None of these. The correct answer is A) 33.33% for chair price less than table price.

When the length is increased by 20%, it becomes 1.2 times the original length. When the width is decreased by 20%, it becomes 0.8 times the original width. The new area is 1.2 × 0.8 = 0.96 times the original area, which is a 4% decrease.

Given the ratio of salaries A:B:C = 1:2:3, let A = x. Then B = 2x and C = 3x. Since B + C = 60000, 2x + 3x = 5x = 60000, so x = 12000. Salary of A = 12000, Salary of C = 36000. The percentage by which C is more than A is ((36000 - 12000) / 12000) * 100 = 200%.

The question is incomplete as it does not specify the base value to which (25/3)% should be applied. Without this, the answer cannot be determined. Therefore, among the given options, 'None of these' is the correct choice.

The original square has side length s, so its area is s². When the length is increased by 40%, the new length becomes 1.4s. When the breadth is increased by 30%, the new breadth becomes 1.3s. The area of the resulting rectangle is therefore 1.4s × 1.3s = 1.82s². This means the new area is 1.82 times the original area, which corresponds to an 82% increase in area. Hence, the correct answer is 82%, which is option B.

The equation is 45 ÷ x = 25% of 90. First, calculate 25% of 90: 0.25 × 90 = 22.5. So the equation becomes 45 ÷ x = 22.5. Solving for x gives x = 45 ÷ 22.5 = 2. Among the options given (5, 6, 7, 8), none is 2, so the correct answer should be 2, which is not listed. The originally given correct answer (B: 6) is incorrect for the equation as stated. Therefore, the correct answer is A: 5 is also incorrect, but since 2 is not an option, the closest correct answer is to fix the options or question. However, based on the equation and calculation, x = 2 is the correct solution. Since 2 is not an option, the question or options need correction. The verified correct answer is A: 5 is not correct, but among the given options, none is correct. The explanation is that the correct solution is x = 2.

If the length of a rectangle is increased by 60%, the new length is 1.6 times the original length. To maintain the same area, the width must be decreased so that the product of the new length and new width equals the original area. Let the fractional decrease in width be y. Then (1.6) × (1 - y) = 1. Solving for y gives y = 0.375, which means the width must be decreased by 37.5%. Among the given options, 37% (option C) is the closest and correct percentage decrease to maintain the same area.

To find 45% of (25% of Rs 1600), first calculate 25% of Rs 1600: 25% of 1600 = 0.25 × 1600 = Rs 400. Then calculate 45% of Rs 400: 45% of 400 = 0.45 × 400 = Rs 180. Therefore, the correct answer is Rs 180, which corresponds to option C.

The factory starts with 3000 ball pens produced in February. Each month, production is reduced by 10%, meaning production in the next month is 90% of the previous month's production. For March (the month after February), production = 3000 × 0.9 = 2700 pens. However, 2700 is not among the options. The closest option is 2190 (option A), which corresponds to production after two months of 10% reductions (i.e., April production = 3000 × 0.9 × 0.9 = 2430, which is also not an option). The option 2187 (option B) corresponds to 3000 × 0.9³, which would be production after three months (May). Since the question asks for March production, the correct calculation is 2700, but since it is not listed, the closest correct option is A (2190), which is the production after two months of reduction (March production should be 2700, but since it's not an option, the question or options are inconsistent). Therefore, the question should be corrected to ask for April production to match option A or options should be adjusted. Given the current options and question, the best corrected answer is A (2190) assuming the question asks for April production.

Given that 16% of a number is 216, we can find the number by dividing 216 by 0.16, which gives 1350. Then, to find 27% of that number, multiply 1350 by 0.27, resulting in 364.5. Therefore, the correct answer is 364.5, which corresponds to option C.

Let the original length be L and width be 2L. Original area = L × 2L = 2L². After increase, length = 1.3L and width = 1.2 × 2L = 2.4L. New area = 1.3L × 2.4L = 3.12L². Percentage increase = ((3.12L² - 2L²) / 2L²) × 100% = (1.12 / 2) × 100% = 56%. None of the given options match this, so the correct answer is 'None of these'.

The total price of the land is Rs. 6 crore 75 lakhs, which equals Rs. 6.75 crore or Rs. 67,500,000. A 2% commission on this amount is 0.02 × 67,500,000 = Rs. 1,350,000, which corresponds to option A.

If 10% of the workers were fired, then 90% remained. Since 540 workers survived, 90% corresponds to 540. Therefore, the total number of workers originally = 540 ÷ 0.9 = 600.

To find the sales tax, multiply the item cost by the tax rate: $2000 × 3% = $2000 × 0.03 = $60. Therefore, the correct tax amount is $60, which corresponds to option B.

Since Rs. 3300 is 75% of the man's monthly income, the full monthly income can be calculated by dividing 3300 by 0.75. This gives 3300 ÷ 0.75 = Rs. 4400. Therefore, the correct monthly income is Rs. 4400, which corresponds to option B.

Let the total number of students be N. The total mean score is 52, so total sum = 52N. The brightest 20% (0.2N students) have a mean score of 80, so their total sum = 0.2N × 80 = 16N. The dullest 25% (0.25N students) have a mean score of 31, so their total sum = 0.25N × 31 = 7.75N. The remaining 55% (0.55N students) have a total sum = 52N - 16N - 7.75N = 28.25N. Therefore, the mean score of the remaining 55% = 28.25N / 0.55N = 51.36 approximately, which corresponds to option C (51.4 approx.). The initial confusion arose from assuming N=100 but miscalculating sums. The algebraic approach confirms option C is correct.

The original carpet has breadth = 6 m and length = 1.44 × 6 = 8.64 m. The new carpet's length is 40% more, so new length = 8.64 × 1.4 = 12.096 m. The new breadth is 25% more, so new breadth = 6 × 1.25 = 7.5 m. The area of the new carpet = 12.096 × 7.5 = 90.72 sq m. The cost of the carpet is area × rate = 90.72 × 45 = Rs. 4082.40. This matches option D. Therefore, the correct answer is D, not B as originally stated. The explanation and calculations confirm option D is correct.

When both the length and width of a rectangle are increased by 20%, the new length and width become 1.2 times their original values. The new area is therefore 1.2 × 1.2 = 1.44 times the original area, which means the area increases by 44%. Hence, the percent increase in the area is 44%.

The total area of the paper is 30 cm × 15 cm = 450 cm². The margins reduce the usable width to 15 cm - 2 × 1.25 cm = 12.5 cm, and the usable height to 30 cm - 2 × 2.5 cm = 25 cm. Therefore, the usable area is 12.5 cm × 25 cm = 312.5 cm². The percentage of the paper area available for typing is (312.5 / 450) × 100 ≈ 69.44%, which is approximately 70%. Hence, the correct answer is option B (70%).

When the side of a square is increased by 25%, the new side length is 1.25 times the original. The area increases by (1.25)^2 = 1.5625, which is a 56.25% increase, so the area increases by 56.25%.

If the length is increased by 60%, the new length is 1.6 times the original. To keep the area the same, the width must be multiplied by 1/1.6 = 0.625, which is a 37.5% decrease.

When the length is increased by 10%, it becomes 1.10 times the original. When the breadth is increased by 25%, it becomes 1.25 times the original. The new area is 1.10 × 1.25 = 1.375 times the original area, which is a 37.5% increase.

When the side of a square is increased by 25%, the new side length is 1.25 times the original. The area increases by (1.25)^2 - 1 = 1.5625 - 1 = 0.5625, or 56.25%.

When the length of the rectangle is increased by 25%, the new length becomes 1.25 times the original length. When the breadth is decreased by 20%, the new breadth becomes 0.8 times the original breadth. The new area is therefore 1.25 × 0.8 = 1.0 times the original area, meaning the area remains unchanged. Hence, the correct answer is 'Remains same'.