Mathematics

Let the average expenditure of all nine men be x. Then the ninth man spends x + 2. The other eight men spend 3 each, so total expenditure is 8*3 + (x + 2) = 24 + x + 2 = x + 26. Since average is total/9, x = (x + 26)/9. Solving gives x = 3.25. Total expenditure = 9 * 3.25 = Rs.29.25. However, this contradicts the initial calculation, so rechecking: 8 men spend 3 each = 24, ninth spends x + 2, average x = (24 + x + 2)/9 = (26 + x)/9, so x = (26 + x)/9 => 9x = 26 + x => 8x = 26 => x = 3.25. Ninth man spends 3.25 + 2 = 5.25. Total = 24 + 5.25 = 29.25. So total money spent is Rs.29.25, which matches option A. Therefore, correct answer is A.

The first ten odd prime numbers are 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31. Their sum is 158. To find the average, divide the sum by 10, which gives 158 ÷ 10 = 15.8. Therefore, the correct answer is 15.8, corresponding to option C.

The total cost of known blankets is (3×100) + (5×150) = 300 + 750 = Rs.1050. Let the unknown rate be x. The average price is given by total cost divided by total blankets: (1050 + 2x) / 10 = 150. Solving gives 1050 + 2x = 1500, so 2x = 450, and x = 225. However, option B is Rs.225, so correct answer is B, not C. Rechecking options: A=150, B=225, C=250, D=None. So correct answer is B.

The total sum of 11 numbers is 11 × 10.9 = 119.9. The sum of the first six numbers is 6 × 10.5 = 63, and the sum of the last six numbers is 6 × 11.4 = 68.4. Since the sixth number is included in both the first six and last six, adding these sums counts the sixth number twice. Therefore, sixth number = (63 + 68.4) - 119.9 = 11.5. However, this calculation yields 11.5, which matches option D. Rechecking the arithmetic: 63 + 68.4 = 131.4; 131.4 - 119.9 = 11.5. So the sixth number is 11.5, which corresponds to option D. The original correct_answer was D, which is correct. The explanation was missing and is now provided. Difficulty is medium as it requires understanding of averages and overlapping sums.

The total sum of 9 observations is 9 × 9 = 81. The sum of the first 5 observations is 5 × 10 = 50, and the sum of the last 5 observations is 5 × 8 = 40. The 5th observation is included in both the first and last 5 observations, so adding these sums gives 50 + 40 = 90, which counts the 5th observation twice. Therefore, the 5th observation = 90 - 81 = 9. However, since the sum of all observations is 81, the 5th observation must be 9 to satisfy both averages. But this contradicts the calculation, so rechecking: sum(first 5) + sum(last 5) = sum(all) + 5th observation, so 50 + 40 = 81 + x, thus x = 9. Therefore, the 5th observation is 9. The correct answer is A.

The total sum of 11 results is 11 × 50 = 550. The sum of the first six results is 6 × 49 = 294, and the sum of the last six results is 6 × 52 = 312. Since the sixth result is included in both the first six and last six results, adding these sums gives 294 + 312 = 606, which counts the sixth result twice. Therefore, the sixth result = 606 - 550 = 56.

The total marks for each batch are calculated by multiplying the number of students by their average marks: (55×50)=2750, (60×55)=3300, and (45×60)=2700. The total number of students is 55+60+45=160. The overall average marks for all students combined is the total marks divided by the total number of students: (2750+3300+2700)/160 = 8750/160 = 54.6875, which rounds to 54.68. Among the given options, 54.68 (option B) is the correct answer.

Since Rs. 3300 is 75% of the man's monthly income, the full monthly income can be calculated by dividing 3300 by 0.75. This gives 3300 ÷ 0.75 = Rs. 4400. Therefore, the correct monthly income is Rs. 4400, which corresponds to option B.

First, find the cost price (CP) using the selling price (SP) of Rs. 50,000 and profit of 17%. CP = SP / (1 + profit%) = 50000 / 1.17 ≈ Rs. 42735. Then, calculate profit when SP = Rs. 47000: Profit = 47000 - 42735 = Rs. 4265. Profit percentage = (4265 / 42735) × 100 ≈ 9.98%. However, this matches option B, so let's re-check calculations: Actually, the profit percentage when sold at Rs. 47000 is less than 17%, so option B is correct. The initial explanation was incorrect; the correct answer is B.

Let the average weight of the first 25 persons be x kg. After adding the new person weighing 46 kg, the average decreases by 5 kg, so the new average is x - 5. The total weight of the first 25 persons is 25x, and the total weight after adding the new person is 25x + 46. The new average is (25x + 46) / 26 = x - 5. Solving this equation gives x = 62 kg.