Mathematics

Let the number be x. According to the question, x exceeds 16% of itself by 42, so x - 0.16x = 42, which simplifies to 0.84x = 42. Solving for x gives x = 42 / 0.84 = 50. However, 50 is option A, so let's re-check the calculation: 16% of 50 is 8, and 50 - 8 = 42, which matches the condition. Therefore, the correct answer is A, not B. Correction: The correct answer is A.

Let the original number be x. The correct operation is to subtract 25% of the number, which is x - 0.25x = 0.75x. The person mistakenly subtracted 25 instead, so his answer was x - 25. According to the problem, this incorrect answer is 25 more than the correct answer, so x - 25 = 0.75x + 25. Solving this equation: x - 0.75x = 25 + 25 => 0.25x = 50 => x = 200. Therefore, the original number is 200, which corresponds to option D.

When the tax is reduced by 20%, the new tax rate is 80% of the original. Consumption increases by 15%, so revenue changes by 0.8 × 1.15 = 0.92, which is an 8% decrease in revenue.

Let the monthly salary be Rs. x. The man saves 20% of his salary, so his initial expenses are 80% of x (0.8x). Due to an increase in the cost of living, his expenses increase by 20%, so new expenses become 1.2 × 0.8x = 0.96x. His new savings are then x - 0.96x = 0.04x, which equals Rs. 200. Solving for x: 0.04x = 200 ⇒ x = 200 / 0.04 = Rs. 5000. Therefore, his monthly salary is Rs. 5000, which corresponds to option A.

Let the third number be 100. Then the first number is 120 (20% more) and the second number is 125 (25% more). The percentage that the first is of the second is (120/125)*100 = 96%.

The original prices of articles X, Y, and Z are in the ratio 8:5:3. After the price increases, the new prices become: - X: 8 × 1.25 = 10 - Y: 5 × 1.20 = 6 - Z: 3 × 1.3333... (33 1/3% = 1/3) = 4 The new ratio is therefore 10 : 6 : 4. Simplifying by dividing each term by 2 gives 5 : 3 : 2, which matches option B. Hence, the correct answer is B.

When Masood's salary is reduced by 10%, it becomes 90% of the original. Increasing this reduced salary by 10% results in 90% × 110% = 99% of the original salary, which is 1% less than the original. Hence, his present salary is 1% less than his previous salary.

To convert a decimal number to a percentage, multiply the decimal by 100 and add the percent sign (%). For 3.5, multiplying by 100 gives 350, so 3.5 expressed as a percentage is 350%. Therefore, the correct answer is option D (350%).

The expenditure change is calculated by multiplying the change in price and quantity. With a 20% increase in tax (price factor 1.20) and a 20% decrease in consumption (quantity factor 0.80), the expenditure factor is 1.20 × 0.80 = 0.96, which is a 4% decrease in expenditure.

The percentage of students failing in at least one subject is calculated using the formula for the union of two sets: P(fail English or fail Math) = P(fail English) + P(fail Math) - P(fail both). Substituting the values: 47% + 54% - 31% = 70%. Therefore, the percentage passing both subjects is the complement of this, which is 100% - 70% = 30%. Hence, the pass percentage in both subjects is 30%, corresponding to option D.