Mathematics

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 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.

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 price increases by 32%, so the new price is 132% of the original. The expenditure increases by 10%, so new expenditure is 110% of the original. Let the new consumption be x kg. Then, 1.32 × x = 1.10 × 10 kg, so x = (1.10 × 10) / 1.32 ≈ 8.33 kg. Hence, option B is correct.

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.

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.

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.

To find 63% of $\frac{25}{7}$, convert 63% to decimal (0.63) and multiply by $\frac{25}{7}$. $0.63\times \frac{25}{7}=\frac{15.75}{7}=2.25$. Therefore, the correct answer is option A, 2.25.

The question states that 20% opted for product A, 60% opted for product B, and the remaining individuals were uncertain. Since the total percentage must be 100%, the uncertain group is 100% - 20% - 60% = 20%. The difference between those who opted for product B and those who were uncertain is given as 720 individuals. This difference corresponds to 60% - 20% = 40% of the total individuals. Therefore, 40% of the total individuals equals 720, so the total number of individuals surveyed is 720 / 0.4 = 1800. Among the options given, 1800 corresponds to option C. Hence, the correct answer is C.

The concept of zero as a number was developed in ancient India, notably by mathematicians like Brahmagupta, not by Al-Khwarizmi or the other options listed. Therefore, none of the given options correctly identify the discoverer of zero.