Averages

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 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.

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.

Let the average before the 17th innings be x. Total runs before 17th innings = 16x. After scoring 85 in the 17th innings, the new average is x + 3. So, (16x + 85)/17 = x + 3. Solving gives x = 33, so the new average is 36.

Let the original average expenditure per student be x. Initially, total expenditure = 100x. After accommodating 20 more students, average decreases by Rs.5, so new average = x - 5. New total expenditure = 120(x - 5) = 120x - 600. Given total expenditure increased by Rs.400, so 120x - 600 = 100x + 400. Solving gives x = Rs.50. Therefore, new total expenditure = 120 * (50 - 5) = 120 * 45 = Rs.5400.

Doubling each student's marks doubles the total sum of marks, so the average also doubles. Since the original average is 36, the new average is 36 × 2 = 72.

The original average is 23. Increasing each of the 10 numbers by 4 increases the total sum by 10 × 4 = 40. The new average is (original total + 40) ÷ 10 = (10 × 23 + 40) ÷ 10 = (230 + 40) ÷ 10 = 270 ÷ 10 = 27.

Three years ago, the total age of the six members was 6 × 19 = 114 years. Today, each member is 3 years older, so total age of original six members is 114 + 6 × 3 = 132 years. Let the boy's age be x. The average age today is (132 + x) / 7. Since the average remains 19, (132 + x) / 7 = 19, so 132 + x = 133, giving x = 1 year. However, this contradicts the calculation. Rechecking: 3 years ago average = 19, so total age = 114. Today, original members aged 3 years each, total 114 + 18 = 132. Average remains 19 with 7 members: total age = 7 × 19 = 133. So, boy's age = 133 - 132 = 1 year. Therefore, the correct answer is A (1 year). The initial answer was A, which is correct. The explanation clarifies the calculation.

The average of 35 numbers is 25, so their total sum is 35 × 25 = 875. If each number is multiplied by 5, the new sum becomes 875 × 5 = 4375. The new average is then 4375 ÷ 35 = 125.

The average of the first 20 natural numbers is calculated by summing them (1+2+...+20 = 210) and dividing by 20, which equals 10.5.

The first 10 odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19. Their sum is 100. The average is calculated as the sum divided by the number of terms, which is 100 / 10 = 10. Therefore, the correct answer is option B (10).

The average age of the group decreased by 3 years when one person aged 42 was replaced by a new person. Since there are 10 persons, the total decrease in the sum of ages is 3 × 10 = 30 years. The difference between the replaced person's age and the new person's age is therefore 30 years. Hence, the new person's age = 42 - 30 = 12 years. This matches option C.

Let the number of clerks be x. The total average salary is given by (2*600 + x*84)/(2 + x) = 90. Solving this equation gives x = 840 clerks. Therefore, the number of clerks is 840, not officers as the question mistakenly asks.

The average age of 8 men increases by 2 years when two women replace two men aged 20 and 24 years. This means the total age of the group increases by 8 × 2 = 16 years. The combined age of the two men replaced is 20 + 24 = 44 years. Therefore, the combined age of the two women is 44 + 16 = 60 years. The average age of the two women is 60 ÷ 2 = 30 years. Hence, the correct answer is 30 years (Option C).

The total wage paid per day is (20×25) + (15×20) + (5×8) = 500 + 300 + 40 = Rs.840. The total number of workers is 20 + 15 + 5 = 40. Therefore, the average wage per day = 840 ÷ 40 = Rs.21.

Let the total number of students be n. The total marks = 39n. Removing four students with marks 5, 12, 15, and 19 reduces total marks by 51 and students by 4, so new average is (39n - 51)/(n - 4) = 44. Solving gives n = 30.

Let the salaries for January, February, March, April, and May be J, F, M, A, and May respectively. Given the average salary for January to April is Rs. 8000, so (J + F + M + A)/4 = 8000, which implies J + F + M + A = 32000. The average salary for February to May is Rs. 8500, so (F + M + A + May)/4 = 8500, which implies F + M + A + 6500 = 34000, so F + M + A = 27500. Subtracting the two sums, we get J + F + M + A - (F + M + A) = 32000 - 27500, which simplifies to J = 4500. Therefore, the salary for January is Rs. 4500, which corresponds to option C.

Let the four numbers be a, b, c, d. The average of the first three numbers is 16, so a + b + c = 48. The average of the last three numbers is 15, so b + c + d = 45. The sum of the first and last numbers is 13, so a + d = 13. Subtracting the second equation from the first gives a - d = 3. Solving the system of equations a + d = 13 and a - d = 3, we get a = 8 and d = 5. Therefore, the last number is 5, which corresponds to option C.

When each number is increased by 5, the mean also increases by 5. Since the original mean is 35, the new mean will be 35 + 5 = 40.

The total sum of the four integers is 69 × 4 = 276. Given the highest integer is 93 and the least is 39, their sum is 132. The remaining two integers sum to 276 - 132 = 144, and their difference is 28. Let the two integers be x and y, with x > y. Then x + y = 144 and x - y = 28. Adding these gives 2x = 172, so x = 86. However, 86 is not among the options except B, but option B is 86. Wait, the options are A:58, B:86, C:49, D:None of these. So the higher integer is 86, which is option B. The original correct_answer is B, which is correct. The explanation was missing, so it is added now. Difficulty is medium due to algebraic reasoning required. Tags added accordingly.

Let the average age of the whole team be x years. The total age of the team is 11x. The captain is 26 years old, and the wicket keeper is 29 years old (3 years older). Excluding these two, the sum of the remaining 9 players' ages is 11x - 26 - 29 = 11x - 55. The average age of these 9 players is (11x - 55)/9, which is given as one year less than the whole team's average, so (11x - 55)/9 = x - 1. Solving this equation gives x = 24 years.

The total amount after the new member joins is 7 × 20 = Rs. 140. The new member contributes Rs. 50, so the total amount before joining was 140 - 50 = Rs. 90. Since there were 6 members before, the average before joining is 90 ÷ 6 = Rs. 15.

Given the sum of five numbers is 655, the average of the first two numbers is 85, so their sum is 2 × 85 = 170. The third number is 125. Therefore, the sum of the first three numbers is 170 + 125 = 295. The sum of the last two numbers is 655 - 295 = 360. The average of the last two numbers is 360 ÷ 2 = 180. Hence, the correct answer is 180, which corresponds to option A.

Let the number of women workers be W. The average age of women is 22 years, and the average age of children is 8 years with 16 children. The combined average age is 15 years. Using the weighted average formula: (22W + 8*16) / (W + 16) = 15. Solving for W gives W = 12. Since 10 women are married, the number of unmarried women is 12 - 10 = 2. However, 2 is not an option, so rechecking the calculation: (22W + 128) = 15(W + 16) => 22W + 128 = 15W + 240 => 7W = 112 => W = 16. Number of unmarried women = 16 - 10 = 6, which matches option D. Therefore, the correct answer is D.

Let the number of boys be B and the number of girls be G. The total age of boys is 16.4B and that of girls is 15.4G. The overall average age is 15.8, so the equation is (16.4B + 15.4G) / (B + G) = 15.8. Multiplying both sides by (B + G) gives 16.4B + 15.4G = 15.8B + 15.8G. Rearranging terms: 16.4B - 15.8B = 15.8G - 15.4G, which simplifies to 0.6B = 0.4G. Dividing both sides by G and then by 0.6 gives B/G = 0.4/0.6 = 2/3. Therefore, the ratio of boys to girls is 2:3, which corresponds to option B.