Mathematics

Subtracting 10% from X means taking away 10% of X, which is equivalent to multiplying X by 90% (or 0.9). This is because 100% - 10% = 90%.

The winner received 62% of the votes and won by 288 votes, meaning the difference between the winner's and loser's votes is 288. Let total votes be x. Then, 62% of x - 38% of x = 288, which simplifies to 24% of x = 288. So, x = 288 / 0.24 = 1200 total votes. The winning candidate's votes are 62% of 1200 = 744 votes. However, 744 is option B, so let's verify carefully: 62% - 38% = 24%, 24% of total votes = 288, total votes = 288 / 0.24 = 1200. Winning votes = 62% of 1200 = 744. Therefore, the correct answer is B, not C. The initial correct_answer was B, which is correct. The explanation was missing and has been added. The question text was corrected for grammar and clarity, and difficulty set to medium.

First, calculate the number of males: 65% of 6400 = 4160. Then, find the number of males at least 50 years old: 25% of 4160 = 1040. Finally, subtract to find males below 50 years: 4160 - 1040 = 3120.

If the price is reduced by 25%, the new price is 75% of the original. To restore the original price, increase the new price by (25/75)*100 = 33 1/3%.

Let F_E be the percentage failing English = 38%, P_U be the percentage passing Urdu = 61%, so failing Urdu = 39%. Given 23% fail both subjects. Total failure percentage = fail English + fail Urdu - fail both = 38% + 39% - 23% = 54%. However, the question asks for actual failure percentage, which is the union of failures. Since 61% pass Urdu, 39% fail Urdu, and 38% fail English, with 23% failing both, total failure = 38% + 39% - 23% = 54%. But the options and question wording suggest actual failure percentage is the union of failures, which is 54%. The correct answer should be 54%, which corresponds to option C. Therefore, the original correct_answer 'C' is correct. The explanation was missing and has been added. Difficulty is medium due to percentage and set operations involved.

If the price is reduced by 25%, the new price is 75% of the original. To restore the original price, the new price must be increased by (25/75)*100 = 33 1/3%.

The population increases at 5% per year. To find the population in 1978 (3 years before 1981), we calculate the population in 1981 divided by (1.05)^3, which gives approximately 120,000. Hence, option A is correct.

If the price increases by 25%, the new price is 125% of the original. To keep expenditure the same, the quantity used must be reduced so that (new quantity) × (new price) = (original quantity) × (original price). This means new quantity = original quantity × (100/125) = 0.8 of original quantity, a 20% reduction.

Let the total marks be M and the passing marks be P. The first student scores 20% of M and fails by 30 marks, so 0.20M = P - 30. The second student scores 32% of M and gets 42 marks more than passing, so 0.32M = P + 42. Subtracting the first equation from the second gives 0.12M = 72, so M = 600. Substituting back, P = 0.20 × 600 + 30 = 150, which is 25% of 600. Therefore, the percentage of marks required to pass is 25%. Hence, the correct answer is B (25%).

Since p is six times q, p = 6q. The difference p - q = 5q. The percent that q is less than p is (difference ÷ p) × 100 = (5q ÷ 6q) × 100 = 83 1/3%.

Let the original fraction be x/y. Increasing numerator by 20% gives 1.2x, decreasing denominator by 25% gives 0.75y. The new fraction is (1.2x)/(0.75y) = 2/15. Simplifying, (1.2/0.75)(x/y) = 2/15, so (1.6)(x/y) = 2/15, hence x/y = (2/15)/1.6 = 2/(15*1.6) = 2/24 = 1/12. Therefore, the original fraction is 1/12, which corresponds to option A.

Under the old scheme, the salesman earned 5% commission on all sales. Under the new scheme, he earns a fixed salary of Rs. 1000 plus 2.5% commission on sales exceeding Rs. 4000. The difference in remuneration is Rs. 600. Setting up the equation and solving for sales gives Rs. 30,000.

When the price is reduced by 10%, the new price is 90% of the original. To restore it to the original price, we need to find the percentage increase on 90% to get back to 100%. The required increase is (10/90)*100 = 11 1/9%.

The total population is 45,000. Males are 5/9 of the population, so males = (5/9) * 45000 = 25,000. Females are the rest, so females = 45000 - 25000 = 20,000. Forty percent of males are married, so married males = 40% of 25,000 = 10,000. Assuming a monogamous society where each married male corresponds to one married female, the number of married females is also 10,000. Therefore, the percentage of married females = (married females / total females) * 100 = (10,000 / 20,000) * 100 = 50%. Hence, the correct answer is 50%.

Let the income be Rs. x. He spends 1/5th on education, so remaining is (4/5)x. Then he spends 20% of the remaining on food, which is 0.2 × (4/5)x = (4/25)x. Amount left after these expenses is x - (1/5)x - (4/25)x = x - (5/25)x - (4/25)x = (16/25)x. Given this amount is Rs.576, so (16/25)x = 576, solving gives x = (576 × 25)/16 = Rs.900. However, this contradicts the options, so rechecking: The leftover after education is (4/5)x, then 20% of this is spent on food, so leftover after food is 80% of (4/5)x = (4/5)x × 0.8 = (4/5) × (4/5)x = (16/25)x. This leftover is Rs.576, so (16/25)x = 576, x = (576 × 25)/16 = Rs.900. Rs.900 is option A, not D. So correct answer is A.

Bilal spends 45% + 25% + 7.5% = 77.5% of his income, so he saves 22.5%. Since 22.5% corresponds to Rs. 9000, his total income is Rs. 9000 ÷ 0.225 = Rs. 40000. However, this calculation shows Rs. 40000, which matches option A, so the original correct answer A is correct. Rechecking: 45% + 25% + 7.5% = 77.5%, remaining 22.5%. 22.5% of income = 9000, income = 9000 / 0.225 = 40000. Therefore, correct answer is A.

If 20% of a number is taken as a reference, then 120% of the same number is 6 times that amount because 120% ÷ 20% = 6. Therefore, if 20% corresponds to 120, then 120% corresponds to 720 (120 × 6).

If the losing candidate got 30% of the votes and lost by 15,000 votes, then the winning candidate got 30% + difference in percentage votes. Let total votes be x. The difference in votes is 15,000 = (winning votes) - (losing votes) = (0.7x) - (0.3x) = 0.4x. So, 0.4x = 15,000, which gives x = 37,500 total votes. The winning candidate got 70% of 37,500 = 26,250 votes. However, the question asks for the number of votes polled by the winning candidate, which is 26,250. The original correct answer was C (26,250), but the options and explanation were inconsistent. On rechecking, the winning candidate's votes are 26,250, so the correct answer is C, not D. Therefore, the original correct answer C is correct. The explanation is now provided, and difficulty is set to medium.

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.

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.

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%).

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.

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.

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%.

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.