1.
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Correct Answer
D. 19
Explanation
The average of 20 numbers is zero, which means that the sum of all these numbers is also zero. In order for the sum to be zero, it is possible for 19 numbers to be greater than zero, as long as the sum of the remaining numbers is negative and cancels out the positive values. Therefore, the maximum number of numbers that may be greater than zero is 19.
2.
Distanc e between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?
Correct Answer
C. 67.2
Explanation
The average speed of the train for the whole journey can be calculated by finding the harmonic mean of the speeds for the two legs of the journey. The time taken for the first leg of the journey (A to B) can be calculated by dividing the distance by the speed, which is 778 km / 84 km/h = 9.26 hours. The time taken for the second leg of the journey (B to A) can be calculated in the same way, which is 778 km / 56 km/h = 13.89 hours. The total time for the whole journey is the sum of these two times, which is 9.26 hours + 13.89 hours = 23.15 hours. The average speed is then calculated by dividing the total distance (2 * 778 km) by the total time (23.15 hours), which is 2 * 778 km / 23.15 hours = 67.2 km/h.
3.
The average age of 30 students is 9 years .If the age of their teacher is included ,it becomes 10 years . The age of the teacher (in years ) is ?
Correct Answer
C. 40
Explanation
The average age of the students is 9 years, which means that the sum of their ages is 9 times 30, or 270 years. When the teacher's age is included, the average becomes 10 years, so the sum of the ages is 10 times 31, or 310 years. To find the age of the teacher, we subtract the sum of the students' ages (270) from the sum of all ages (310), which gives us 40 years.
4.
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Correct Answer
A. 4991
Explanation
To find the sale amount in the sixth month, we need to calculate the total sale for the 6 months. The average sale for 6 months should be Rs. 6500.
Total sale for 5 months = Rs. 6435 + Rs. 6927 + Rs. 6855 + Rs. 7230 + Rs. 6562 = Rs. 34009
To find the sale amount in the sixth month, we subtract the total sale for 5 months from the target average sale of 6 months multiplied by 6.
Target average sale for 6 months = Rs. 6500
Total sale for 6 months = Rs. 6500 * 6 = Rs. 39000
Sale amount in the sixth month = Total sale for 6 months - Total sale for 5 months
= Rs. 39000 - Rs. 34009
= Rs. 4991
Therefore, the sale amount in the sixth month must be Rs. 4991 to achieve an average sale of Rs. 6500.
5.
The avearage age of boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is?
Correct Answer
D. None of these
Explanation
The average age for the whole class cannot be determined based on the given information. The question does not provide the number of boys and girls in the class, so it is not possible to calculate the overall average age. Therefore, the correct answer is "none of these".
6.
After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago.what is the difference between the ages of the replaced and the new member ?
Correct Answer
B. 15
7.
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Correct Answer
C. 6.25
Explanation
To find the run rate in the remaining 40 overs, we need to consider the total number of runs required and the number of overs remaining. The target is 282 runs, and the first 10 overs had a run rate of 3.2. This means that in the first 10 overs, 32 runs were scored. To reach the target of 282 runs, there are 40 overs remaining. Therefore, the remaining runs required are 282 - 32 = 250. The run rate needed in the remaining overs is the remaining runs divided by the remaining overs, which is 250/40 = 6.25.
8.
Three years ago , the average age of A, B and C was 27 years and that of B and C, 5 years ago was 20 years. A’s present age is ?
Correct Answer
A. 40
Explanation
Three years ago, the average age of A, B, and C was 27 years. This means that the sum of their ages three years ago was 27 multiplied by 3, which is 81.
Five years ago, the average age of B and C was 20 years. This means that the sum of their ages five years ago was 20 multiplied by 2, which is 40.
To find A's present age, we need to subtract the sum of B and C's ages five years ago from the sum of A, B, and C's ages three years ago.
81 - 40 = 41.
Since this is the age three years ago, we need to add 3 to get A's present age.
41 + 3 = 44.
Therefore, A's present age is 44.
9.
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Correct Answer
D. 19
Explanation
If the average of 20 numbers is zero, it means that the sum of all the numbers is also zero. In order for the sum to be zero, some numbers must be positive and some must be negative. However, the number of positive numbers cannot exceed the number of negative numbers, as that would result in a positive sum. Therefore, at most, there can be 19 numbers greater than zero, with one number being zero to balance out the sum.
10.
The avearge age of 36 students in a group is 14 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years?
Correct Answer
D. 51
Explanation
If the average age of 36 students is 14 years, then the total age of all the students is 36 * 14 = 504 years. When the teacher's age is included, the average increases by one, which means the total age of all the students and the teacher is now 505 years. Since the teacher's age is included, the teacher's age must be 505 - 504 = 1 year. Therefore, the teacher's age is 51 years.