Question for Practice Questions Level 2: Averages - 1
Try yourself:The average score of a cricketer in a certain number of innings is 15. When he scores zero in the next innings, his average drops to 13.5. How many innings have been played by him, including the last one?
Explanation
Let the number of innings be x.
Total runs scored by the cricketer = 15x
New number of innings = x + 1
Also, new average = 13.5
15x = 13.5(x + 1)
15x = 13.5x + 13.5
15x - 13.5x = 13.5
1.5x = 13.5
Number of innings played, including the last one = 9 + 1 = 10
Question for Practice Questions Level 2: Averages - 1
Try yourself:The average of three distinct positive integers is 11. What can be the maximum possible value that the greatest number of these three can take?
Explanation
To get the greatest possible value for one number, the other two should be as small as possible sum of the three numbers = 33.
Since the numbers are positive distinct integers, the two numbers can be 1 and 2.
So, the third will be 30, which is the maximum possible value.
Question for Practice Questions Level 2: Averages - 1
Try yourself:The average of 3 numbers is x. If the second number is 9 more than the first and the third number is 5 more than x, then what is the difference between x and the first number?
Explanation
Let a, b and c be the three numbers.
a + b + c = 3x
b = 9 + a and c = x + 5
a + a + 9 + x + 5 = 3x
2a + 14 = 2x
∴ x - a = 7
Question for Practice Questions Level 2: Averages - 1
Try yourself:In a History test, the boys' average is 86 points and the girls' average is 80 points. If the overall average of the class is 82 points, what is the ratio of the number of boys to that of girls in the class?
Explanation
Let the number of boys in the class be 'b' and the girls be 'g'.
Now, as the average score is 82, we have (86b + 80g)/(b + g) = 82
86b + 80g = 82b + 82g
4b = 2g
b/g = 1/2
Thus the required ratio is 1 : 2.
Hence, answer option (4) is correct.
Question for Practice Questions Level 2: Averages - 1
Try yourself:A certain company employed 600 men and 400 women and the average wage was Rs. 2.55 per day. If a woman got 50 paise less than what a man got, then what were their daily wages?
Explanation
Total employees = 600 + 400 = 1000
Total income at an average Rs. 2.55/day = 2.55 × 1000 = Rs. 2550 per day
Let the daily wage of a man be Rs. x.
Then, their total wages = Rs. 600x
A woman got 50 paise less than a man.
∴ Their total wages = 400(x - 0.5)
⇒ 600x + 400(x - 0.5) = 2550
⇒ 600x + 400x - 200 = 2550
⇒ 1000x = 2750
⇒ x = Rs. 2.75
∴ Man`s daily wage = Rs. 2.75
Woman`s daily wage = 2.75 - 0.50 = Rs. 2.25
Question for Practice Questions Level 2: Averages - 1
Try yourself:What is the average of all the two-digit numbers that are divisible by 3, 6 and 9?
Explanation
Numbers that are divisible by 3, 6 and 9 = Multiple of L.C.M(3, 6, 9) = 18, 36, 54,......
The required numbers are 18, 36, 54, … and 90.
Question for Practice Questions Level 2: Averages - 1
Try yourself:The average of n consecutive numbers is 'a'. If any one number is deleted from these 'n' numbers, then the average of the remaining (n – 1) numbers cannot be less than
Explanation
Let x, x + 1, x + 2, ...., (x + n) be n consecutive integers, then their sum is
Assume after deleting any term, the new mean is , then their sum is
Subtract equation (1) from equation (2) we get
So, the answer is a - 1/2
Question for Practice Questions Level 2: Averages - 1
Try yourself:The average of 21 results is 54. If the average of the first 11 results is 51 and that of the last 11 is 57, find the 11^{th} result.
Explanation
Average of 21 results = 54
Total of 21 results = 54 x 21 = 1134
Average of the first 11 results = 51
Total of the first 11 results = 51 x 11 = 561
Average of the last 11 results = 57
Total of the last 11 results = 57 x 11 = 627
Therefore, 11th result = 561 + 627 - 1134 = 1188 - 1134 = 54
Question for Practice Questions Level 2: Averages - 1
Try yourself:The average of 10 numbers is 20. If a number equal in value to the largest of the 10 given numbers is added to the given set, the average increases by 1. But instead of adding the number, if the largest number itself is deleted, then what will be the average?
Explanation
Sum of 10 numbers = 200
Assume that x is the maximum.
If x is deleted, average
Question for Practice Questions Level 2: Averages - 1
Try yourself:Some children are sitting in a row. The n^{th} child has n^{2} chocolates and every child has an average of 46 chocolates. How many children are sitting in the row?
Explanation
According to the question,
Total number of chocolate = 46n
2n^{2} + 2n + n + 1 = 276
2n^{2} + 3n - 275 = 0