Mathematics

Let the two consecutive positive integers be n and n+1. The sum of their squares is n^2 + (n+1)^2, and their product is n(n+1). According to the problem, n^2 + (n+1)^2 = n(n+1) + 91. Simplifying, we get 2n^2 + 2n + 1 = n^2 + n + 91, which reduces to n^2 + n - 90 = 0. Solving this quadratic equation gives n = 9 or n = -10 (discard negative). Thus, the integers are 9 and 10. Checking the original condition: 9^2 + 10^2 = 81 + 100 = 181; their product is 90; 181 - 90 = 91, which matches the problem statement. Therefore, the correct answer is A (9, 10).

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.

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 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.

Masood sells the plot to Aftab at a 20% profit, so Aftab's cost price = 8000 + 20% of 8000 = 8000 + 1600 = Rs. 9600. Aftab sells to Zahid at a 20% loss, so Zahid's cost price = 9600 - 20% of 9600 = 9600 - 1920 = Rs. 7680.

The two automobiles are moving toward each other with a combined speed of 60 km/h + 40 km/h = 100 km/h. To cover the 150 km distance between them, the time taken is distance divided by speed, which is 150 km ÷ 100 km/h = 1.5 hours. Therefore, the correct answer is 1.5 hours.

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.

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).

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 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.