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The MCQs below are drawn from the Mathematics subject category.
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7611
The average salary of 20 workers in an office is Rs. 15,000 per month. If the manager's salary is added, the average salary becomes Rs. 16,000. What is the manager's monthly salary?
For the average of 30 numbers to be zero, their total sum must be zero. It is possible for 29 numbers to be strictly greater than zero (positive), as long as the 30th number is a sufficiently large negative number to cancel out their sum. Thus, at most 29 can be greater than zero.
7613
A batsman has a certain average of runs for 11 innings. In the 12th inning, he makes a score of 90 runs, thereby increasing his average by 5. What is his average after the 12th inning?
Let the original average for 11 innings be 'x'. Total runs = 11x. After 12 innings, the average is 'x + 5'. Equation: (11x + 90) / 12 = x + 5. 11x + 90 = 12x + 60. Solving this gives x = 30. His new average after 12th inning is x + 5 = 30 + 5 = 35.
7614
A student's marks were wrongly entered as 83 instead of 63. Due to this error, the average marks of the class increased by half a mark (0.5). How many students are there in the class?
The difference in marks due to the wrong entry is 83 - 63 = 20. This extra 20 marks caused an overall increase of 0.5 marks per student. Number of students = Total increase in marks / Increase per student = 20 / 0.5 = 40 students.
7615
In a family, the average age of a father and a mother is 35 years. The average age of the father, mother, and their only son is 27 years. What is the age of the son?
Total age of father and mother = 2 * 35 = 70 years. Total age of father, mother, and son = 3 * 27 = 81 years. The age of the son is the difference between these two totals: 81 - 70 = 11 years.
7616
The average temperature for Monday, Tuesday, and Wednesday was 40°C. The average for Tuesday, Wednesday, and Thursday was 41°C. If the temperature on Thursday was 42°C, what was the temperature on Monday?
Total sum of all 11 results = 11 * 50 = 550. Sum of the first 6 results = 6 * 49 = 294. Sum of the last 6 results = 6 * 52 = 312. The sixth result is counted twice when adding these two sums. Sixth result = (294 + 312) - 550 = 606 - 550 = 56.
7618
The average age of a class of 30 students is 15 years. If the teacher's age is included, the average age increases by 1 year. What is the age of the teacher?
Total age of 30 students = 30 * 15 = 450 years. With the teacher, there are 31 people, and the new average is 16 years. Total age of 31 people = 31 * 16 = 496 years. Teacher's age = 496 - 450 = 46 years.
7619
The average weight of 8 men is increased by 1.5 kg when one of the men who weighs 65 kg is replaced by a new man. What is the weight of the new man?
The total weight increase for all 8 men is 8 * 1.5 kg = 12 kg. This increase happens because the new man is heavier than the man he replaced. Weight of the new man = weight of the replaced man + total increase = 65 kg + 12 kg = 77 kg.
7620
The average of 5 numbers is 27. If one number is excluded, the average becomes 25. What is the excluded number?
The total sum of the initial 5 numbers = 5 * 27 = 135. After excluding one number, there are 4 numbers, and their sum = 4 * 25 = 100. The excluded number is the difference of the sums: 135 - 100 = 35.
