Mathematics

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.

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 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.

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.

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.

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%.

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).

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.

The selling price of each bicycle is Rs.990. For the first bicycle, with a 10% profit, cost price = 990 / 1.1 = Rs.900. For the second bicycle, with a 10% loss, cost price = 990 / 0.9 = Rs.1100. Total cost = 900 + 1100 = Rs.2000. However, this contradicts the options, so rechecking: 10% profit means SP = 110% of CP, so CP = SP / 1.1 = 900; 10% loss means SP = 90% of CP, so CP = SP / 0.9 = 1100; total cost = 900 + 1100 = Rs.2000. Option A is Rs.2000, so correct answer is A, not B. Correction made accordingly.

The cost price of one pen is Rs.9/8 = Rs.1.125. The selling price of one pen is Rs.8/9 ≈ Rs.0.8889. Since the selling price is less than the cost price, there is a loss. The loss percentage = ((1.125 - 0.8889)/1.125) × 100 ≈ 20.98%.