Quantitative Apptitude - Average Online Test 10

Explanation
The average age of the class is 15 years, which means the total age of all the students combined is 39 * 15 = 585 years. When the age of the teacher is included, the average increases by 3 months, which is equivalent to 1/4 of a year. So, the new average age becomes 15 + 1/4 = 15.25 years. The total age of all the students and the teacher combined is now 40 * 15.25 = 610 years. The age of the teacher can be found by subtracting the total age of the students from the total age of the class, which is 610 - 585 = 25 years.

Explanation
If the average age of 36 students in a group is 14 years, then the total age of all the students combined is 36 * 14 = 504 years. When the teacher's age is included, the average increases by one. This means that the total age of all the students and the teacher combined is now 505 years. Since the teacher's age is the difference between the two totals, the teacher's age is 505 - 504 = 1 year. Therefore, the teacher's age is 51 years.

Explanation
When the average weight of the oarsmen increases by 1.8 Kgs, it means that the total weight of the oarsmen has increased by 10 x 1.8 = 18 Kgs. Since one crew member weighing 53 Kgs is replaced by a new man, the weight of the new man can be found by subtracting 18 from 53. Therefore, the weight of the new man is 53 - 18 = 35 Kgs.

Explanation
When the pupil's marks were wrongly entered as 83 instead of 63, the average marks for the class increased by half. This means that the pupil's marks were 20 more than they should have been (83 - 63 = 20). Since the average increased by half, this means that there must have been 40 pupils in the class (20 x 2 = 40). Therefore, the correct answer is 40.

Explanation
The original expenditure of the mess was 420. This can be determined by setting up an equation based on the given information. Let the original expenditure per day be x. The total expenditure before the admission of new students is 35x. After the admission of 7 new students, the total expenditure becomes (35+7)(x+42). The average expenditure per head before the admission is 35x/35 = x. After the admission, the average expenditure per head becomes (35+7)(x+42)/42 = x-1. Solving these equations, we get x = 420, which is the original expenditure of the mess.

Explanation
In order to increase his average by 6 runs, the cricketer must have scored a total of 6 x 11 = 66 runs in the 11 innings. Since he scored 108 runs in the 11th inning, his previous total score for the 10 innings must have been 108 - 66 = 42 runs. Therefore, his average for the 10 innings was 42/10 = 4.2 runs per inning. Adding the 6 runs increase, his new average is (4.2 + 6) = 10.2 runs per inning, which can be rounded to 48.

Explanation
In order to find the average after the 17th inning, we need to consider the average before the 17th inning. Since the batsman increased his average by 3 runs after the 17th inning, we can subtract 3 from the average before the 17th inning to find the new average. Therefore, the average after the 17th inning is 39.

Explanation
The average speed of the train during the whole journey can be found by taking the total distance traveled and dividing it by the total time taken. The train travels a distance of 778 km from A to B at a speed of 84 km/h, which takes 778/84 = 9.26 hours. The return journey from B to A is also 778 km, but at a speed of 56 km/h, which takes 778/56 = 13.89 hours. Therefore, the total time taken for the whole journey is 9.26 + 13.89 = 23.15 hours. The average speed is then calculated as the total distance (1556 km) divided by the total time (23.15 hours), which is 1556/23.15 = 67.2 km/h.

Explanation
The average age of the boys in the class is twice the number of girls in the class. Given that the ratio of boys to girls is 5:1, we can assume that there are 30 boys and 6 girls in the class. Since the average age of the boys is twice the number of girls, we can calculate the total age of the boys by multiplying the average age by the number of boys, which is 2 * 6 = 12. Therefore, the total age of the boys in the class is 12 * 30 = 360.

Explanation
The average of the eight numbers is 14, which means that the sum of all eight numbers is 8 multiplied by 14, which equals 112. The average of six of these numbers is 16, which means that the sum of these six numbers is 6 multiplied by 16, which equals 96. To find the sum of the remaining two numbers, we subtract the sum of the six numbers from the sum of all eight numbers: 112 - 96 = 16. Since there are two remaining numbers, we divide the sum by 2 to find the average, which is 16 divided by 2, equaling 8. Therefore, the average of the remaining two numbers is 8.