Mathematics

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.

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).

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.

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.

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%.

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%.

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.

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.

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 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%).