Average problems
- 1. The average age of 5 member of a committee is the same is it was 3 years ago ,because an old member has been replaced by a new member . the difference between the age of old and new member is?
Options- A. 2 years
- B. 4 years
- C. 8 years
- D. 15 years Discuss
Correct Answer: 15 years
Explanation:
Increase in sum of age during 3 years = 3 x 5 years
= 15 years
So , the difference between ages of old and new member is 15 years
- 2. The average age of 11 players of a cricket is decreased by two month when two of them aged 17 years and 20 years are replaced by two reserves . the average of the reserves is?
Options- A. 17 years 1 month
- B. 17 years 7 month
- C. 17 years 11 months
- D. 18 years 3 months Discuss
Correct Answer: 17 years 7 month
Explanation:
Decrease in sum of age = 11 x 2 months
= 1 year 10 months
Total age of reserves = (17 + 20 ) years - (1 year 10 month)
= 35 years 2 months
Average age of the reserves = (35 years 2 months ) / 2
= 17 years 7 months
- 3. 5 years ago, the average of Ram and Shyam age was 20 years. now, the average age of Ram , Shyam and Mohan is 30 years . what will be Mohan's age 10 years hence?
Options- A. 45 years
- B. 50 years
- C. 49 years
- D. 60 years Discuss
Correct Answer: 50 years
Explanation:
Total age of Ram and shyam 5 years ago
= 2 x 20 = 40 years
? Total age of Ram and Shyam at present
= 40 + 5 + 5 = 50 years
Mohan's age now =90 - 50 years = 40 years
Mohan's age 10 years hence = 40 + 10 years
= 50 years
- 4. The average of A and B is 20 years. If C were to replace A, the average would be 19 and if C were to replace B, the Average would be 21. What are the ages of A, B and C?
Options- A. 22, 18, 20
- B. 18, 22, 20
- C. 20, 22, 18
- D. 18, 20, 22 Discuss
Correct Answer: 20, 22, 18
Explanation:
Let a, b, c are the ages of A, B and C respectively
a + b = 2 X 20 = 40 ...(1)
b + c = 2 x 19 = 38 ...(2)
c + a = 2 x 21 = 42 ...(3)
Adding all the 3 equalities
2a + 2b + 2c = 120
a + b + c = 60 --- (4)
From eq. (2) and (4)
a = 22
From eq. (1) and (4)
b = 18
From eq. (4)
c= 20
? Age of A = 22 years
Age of B = 18 years
Age of C = 20 years
- 5. What will be the average of even numbers between 11 to 63.
Options- A. 37.5
- B. 47
- C. 42
- D. 37 Discuss
Correct Answer: 37
Explanation:
Even numbers between 11 to 63
= 12,14,16,18,20,..........,62.
Clearly, this is a series of consecutive even number
According to the formula
Average of consecutive even numbers = (First number + Last number)/2
= (12 + 62)/2
= 74/2
= 37
- 6. Calculate the average of the cubes of first five natural numbers.
Options- A. 55
- B. 65
- C. 45
- D. 35 Discuss
Correct Answer: 45
Explanation:
As per the formula,
Average of the cubes os 1st 'n' natural numbers= n(n+1)2/4
where, n= 5.
? Required average = 5(5+1)2/4
= (5 x 36)/4 = 5 x 9= 45
- 7. The average of 8 numbers is 14. The average of 6 of these numbers is 16. What is the average of the remaining two numbers?
Options- A. 12
- B. 6
- C. 8
- D. 10 Discuss
Correct Answer: 8
Explanation:
Average of 8 numbers = 14
Sum of 8 numbers = 14 x 8 = 112
Similarly, average of 6 numbers = 16
Sum of 6 number = 16 x 6 = 96
? Sum of remaining two number
= Sum of 8 number - sum of 6 numbers
= 112- 96 = 16
Average = (sum of two number)/2 = 16/2 = 8
- 8. Average age of 5 boys is 16 yr,of which that of 4 boys is 16 yr, 3 months. The age of the 5th boys.
Options- A. 15yr
- B. 15yr 6 months
- C. 15 yr 4 months
- D. 15 year 2 months Discuss
Correct Answer: 15yr
Explanation:
Average of 5 boys = 16 yr
sum of age of 5 boys = 16 x 5 = 80 yr
? Average age of 4 boys = 16 - yr 3 month
= 16 yr + 3/12 yr = 16 yr + 1/4 yr
Sum of ages of 4 boys = 4 x (16 +1/4) yr
= 64 +1 = 65 yr
? Age of 5th boy = (80 - 65) yr = 15 yr
- 9. Eight consecutive numbers are given. If the average of the two number that appear in the middle is 6 then the sum of the eight given numbers is
Options- A. 36
- B. 48
- C. 54
- D. 64 Discuss
Correct Answer: 48
Explanation:
Let's eight sequentially number are x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6 and x + 7.
According to the question [(x + 3) + (x + 4)]/2 = 6
? (2x + 7)/2 = 6 ? 2x + 7 = 12
? 2x = 5 ? x = 5/2
? Sum of all eight numbers = x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7
= 8x + 28
= 20 + 28
= 48
- 10. The average of 4 consecutive even numbers is 27. What is the greatest number
Options- A. 28
- B. 26
- C. 32
- D. 30 Discuss
Correct Answer: 30
Explanation:
Let the four consecutive even number are x, ( x+2), (x+4), (x+6).
Clearly this is a series of consecutive even numbers
According to the formula,
Average of consecutive numbers = (first number + last number)/ 2
? 27 = [x + (x + 6)]/2
? x + 3 = 27
? x =24
? Greatest number = 4th consecutive even number = (x + 6) = 24 + 6 = 30
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