Mathematics

Calculating the number of men and women who cleared the final test shows more men succeeded overall. Although women's success rates at each stage are higher, the larger initial number of men results in more men clearing the examination.

Let the total number of voters be N. 10% did not vote, so votes cast = 0.9N. Of these, 10% were invalid, so valid votes = 0.9N × 0.9 = 0.81N. The winning candidate got 54% of valid votes = 0.54 × 0.81N = 0.4374N. The other candidate got 46% of valid votes = 0.46 × 0.81N = 0.3726N. The majority is the difference: 0.4374N - 0.3726N = 0.0648N = 1620. Solving for N gives N = 1620 / 0.0648 = 25000. However, this contradicts the options. Rechecking calculations: 10% did not vote → votes cast = 0.9N; 10% of votes polled invalid → valid votes = 0.9N × 0.9 = 0.81N; majority = (54% - 46%) × 0.81N = 8% × 0.81N = 0.0648N = 1620; N = 1620 / 0.0648 = 25000. Since 25000 is option A, correct answer is A, not B. Therefore, correct answer is A (25000).

When selling two goats at the same price, one with a 10% profit and the other with a 10% loss, the overall effect is a loss. This is because the cost prices differ, and the combined transaction results in a net loss of approximately 1%.

The list price is Rs. 65. After the first discount of 10%, the price becomes 65 × 0.90 = Rs. 58.5. The customer pays Rs. 56.16 after the second discount. Let the second discount be x%. Then, 58.5 × (1 - x/100) = 56.16. Solving for x gives (1 - x/100) = 56.16 / 58.5 ≈ 0.96, so x ≈ 4%. Therefore, the other discount is 4%, which corresponds to option B.

Loss = Cost Price - Selling Price = 1500 - 1230 = 270. Loss % = (Loss / Cost Price) × 100 = (270 / 1500) × 100 = 18%. However, option A is 18%, so correct answer is A, not C. Rechecking calculation: 270/1500=0.18=18%. So correct answer is A.

Given that the cost price of 13 articles equals the selling price of 11 articles, the selling price of one article is (cost price of 13 articles) / 11 = (13/11) times the cost price of one article. The profit per article is therefore (13/11 - 1) = 2/11 of the cost price. The profit percentage is (2/11) × 100 = 18 2/11%. Hence, the correct answer is option B.

The trader marks the price 20% above cost price, so Marked Price = 1.2 × Cost Price. A 5% discount on the marked price means Selling Price = 0.95 × Marked Price = 0.95 × 1.2 × Cost Price = 1.14 × Cost Price. The gain is Rs.8400, so Gain = Selling Price - Cost Price = 0.14 × Cost Price = 8400. Therefore, Cost Price = 8400 / 0.14 = Rs.75000.

Given that the cost price (C.P) of 10 pens is equal to the selling price (S.P) of 12 pens, the selling price of one pen is less than its cost price, indicating a loss. Calculation: Let the cost price of one pen be C.P = x. Then, cost price of 10 pens = 10x. Selling price of 12 pens = 10x (given equal to cost price of 10 pens). So, selling price of one pen = (10x) / 12 = (5x) / 6. Loss per pen = C.P - S.P = x - (5x/6) = x/6. Loss percentage = (Loss / C.P) * 100 = (x/6) / x * 100 = 100/6 = 16 2/3 % loss. Therefore, the correct answer is option C: 16 2/3% loss.

Let the selling price be S and cost price be C. Selling at 2/3 S causes a 20% loss, so (2/3)S = 0.8C, which gives C = (2/3)S / 0.8 = (5/6)S. Profit percent when selling at S is ((S - C)/C)*100 = ((S - (5/6)S)/(5/6)S)*100 = (1/6)/(5/6)*100 = (1/5)*100 = 20%. However, this contradicts the options, so rechecking: Actually, C = (2/3)S / 0.8 = (2/3)S * (1/0.8) = (2/3)S * (5/4) = (5/6)S. Profit % = ((S - C)/C)*100 = ((S - (5/6)S)/(5/6)S)*100 = (1/6)/(5/6)*100 = (1/5)*100 = 20%. So profit percent is 20%, matching option A. But option A is 20%, so correct answer is A, not B. Therefore, correct answer is A.

Let the number of children be x. Each child receives 20% of x sweets, i.e., 0.2x sweets. Total sweets distributed = number of children × sweets per child = x × 0.2x = 0.2x². Given total sweets = 605, so 0.2x² = 605 ⇒ x² = 3025 ⇒ x = 55. Each child receives 0.2 × 55 = 11 sweets. This matches option A. Therefore, the correct answer is 11 sweets per child.

Let the original cost price be Rs. x. The selling price with 20% profit is 1.2x. If bought at 20% less, cost price is 0.8x, and selling price is (1.2x - 75). Given this selling price yields 25% profit on 0.8x, so (1.2x - 75) = 1.25 * 0.8x = 1.0x. Solving 1.2x - 75 = x gives 0.2x = 75, so x = 375. However, this contradicts the calculation. Rechecking: 1.2x - 75 = 1.25 * 0.8x = 1.0x, so 1.2x - 75 = x, 0.2x = 75, x = 375. So original cost price is Rs.375, which matches option B. Therefore, correct answer is B. The initial explanation was missing; this explanation clarifies the solution.

Given that selling the house for Rs.45000 results in a gain of 1/8 of the cost price, the cost price (outlay) can be calculated as: Cost Price = Selling Price / (1 + Gain Fraction) = 45000 / (1 + 1/8) = 45000 / 1.125 = Rs.40000. To find the selling price for a 5% loss, multiply the cost price by 0.95: 40000 × 0.95 = Rs.38000. Therefore, the selling price to incur a 5% loss should be Rs.38000, which corresponds to option B.

To dilute 9 ml of lotion containing 50% alcohol to a lotion containing 30% alcohol, use the dilution formula C1V1 = C2V2, where C1 = 50%, V1 = 9 ml, C2 = 30%, and V2 is the final volume after dilution. Calculating: 50% × 9 ml = 30% × V2 → 4.5 = 0.3 × V2 → V2 = 4.5 / 0.3 = 15 ml. The volume of water to add is the final volume minus the initial volume: 15 ml - 9 ml = 6 ml. Therefore, 6 ml of water should be added, which corresponds to option D.

Ram spends 65% of Rs. 720, which is 0.65 × 720 = Rs. 468. Therefore, he saves Rs. 720 - Rs. 468 = Rs. 252.

Given the total population is 300,000 with 180,000 males, the number of females is 120,000. Since 50% of the population is illiterate, the literate population is 50% of 300,000, which is 150,000. Among males, 70% are literate, so literate males = 70% of 180,000 = 126,000. Therefore, literate females = total literate - literate males = 150,000 - 126,000 = 24,000. This matches option A.

Let the cost price be Rs. x. Selling at 10% loss means selling price = 0.9x. If sold for Rs.140 more, selling price = 0.9x + 140, which equals a 4% gain, so 1.04x = 0.9x + 140. Solving gives x = Rs. 3500. However, this conflicts with options, so re-check: 1.04x - 0.9x = 140 => 0.14x = 140 => x = 1000. So cost price is Rs.1000, which matches option A. Therefore, correct answer is A.

The total purchase amount is Rs. 25, which includes taxable and tax-free items. The sales tax paid is Rs. 0.30, and the tax rate is 6%. To find the taxable amount before tax, divide the tax paid by the tax rate: 0.30 / 0.06 = Rs. 5. This Rs. 5 is the cost of taxable items before tax. The total cost of taxable items including tax is Rs. 5 + Rs. 0.30 = Rs. 5.30. Therefore, the cost of tax-free items is the total purchase minus the total cost of taxable items including tax: 25 - 5.30 = Rs. 19.70. Hence, the correct answer is Rs. 19.70 (Option C).

If the price increases by 20%, to keep expenditure constant, consumption must decrease so that (1 + price increase) × (1 - consumption decrease) = 1. Solving, consumption decrease = 20/120 = 1/6 = 16 2/3%.

Given that 8% of the voters did not cast their votes, 92% of the total voters actually voted. The winner obtained 48% of the total votes, so the loser got 44% (92% - 48%) of the total votes. The difference between the winner and the loser is 4% of the total voters, which equals 1100 votes. Therefore, the total number of voters is 1100 divided by 0.04, which equals 27,500. This matches option D, making it the correct answer.

First, calculate the rebate: 6% of Rs. 6650 = Rs. 399. So, the price after rebate = 6650 - 399 = Rs. 6251. Then, calculate sales tax: 10% of Rs. 6251 = Rs. 625.10. Total amount to pay = 6251 + 625.10 = Rs. 6876.10.

Starting with 17xy + 7 = 19xy, subtract 17xy from both sides to get 7 = 2xy. Dividing both sides by 2 gives xy = 7/2. Multiplying both sides by 4 gives 4xy = 4 * (7/2) = 14. However, since the options do not include 14 as the correct answer for 4xy, let's re-examine. The original equation is 17xy + 7 = 19xy. Subtract 17xy: 7 = 2xy, so 2xy = 7, then xy = 7/2. Then 4xy = 4 * (7/2) = 14, which matches option D. Therefore, the correct answer is D, not A. The initial correction was incorrect. The original correct_answer D is correct. Explanation updated accordingly.

Using the formula for union of two sets: P(Car or Mobile) = P(Car) + P(Mobile) - P(Both) = 80% + 60% - 55% = 85%. Therefore, 85% of those surveyed owned a car or a mobile phone or both.

Let the total percentage of students be 100%. Given 18% play neither football nor cricket, so 82% play football or cricket or both. Using the formula for union of two sets: P(F ∪ C) = P(F) + P(C) - P(F ∩ C), we have 82% = 40% + 50% - P(F ∩ C). Solving gives P(F ∩ C) = 8%.

Using the principle of inclusion-exclusion, the percentage reading at least one magazine is 45% + 55% + 40% - 30% - 15% - 25% + 10% = 80%. Therefore, 20% do not read any magazine.

Let Y's pay be Rs. y. Then X's pay is 120% of y, i.e., 1.2y. The total pay is y + 1.2y = 2.2y = 550. Solving for y gives y = 550 / 2.2 = 250. Hence, Y is paid Rs. 250 per week.