Question 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The average age of 5 member of a committee is the same is it was 3 years ago ,because an old member has been replaced by a new member .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?

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 5

What will be the average of even numbers between 11 to 63.

Accepted Answer

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

Question 6

Calculate the average of the cubes of first five natural numbers.

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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.

Accepted Answer

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

Question 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

Accepted Answer

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

Question 10

The average of 4 consecutive even numbers is 27. What is the greatest number

Accepted Answer

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

Question 11

A businessman purchased 30 TV sets in ₹ 300000, If the average cost of 15 TV sets is ₹ 9000 then find out the average cost of remaining TV sets.

Accepted Answer

Total cost of 30 TV sets = ₹ 300000 Total cost of 15 TV sets = 9000 x 15 = 135000 Total cost of remaining 15 TV sets = 300000 - 135000 = 165000 ∴ Average cost of remaining TV sets = 165000/15 = ₹ 11000

Question 12

The average age of 30 girls is 13 yr. The average of first 18 girls is 15 yr. Find out the average age of remaining 12 girls.

Accepted Answer

Total age of 30 girls = 30 x 13 = 390 yr Total age of 18 girls = 18 x 15 = 270 yr. ∴ Age of remaining 12 girls = 390 - 270 = 120 yr ∴ Required average = 120/12 = 10 yr

Question 13

The average of four consecutive numbers A, B, C, and D is 49.5. What is the product of B and D?

Accepted Answer

Let the numbers A, B, C, and D are N , N+1, N + 2 and N + 3, respectively. According to the question, [N + (N+1) + (N+2) + (N+3)] / 4 = 49.5 ⇒ 4N + 6 = 4 x 49.5 ⇒ 4N = 198 - 6 ⇒ N = 192/4 ⇒ N = 48 The required product = B x D = (N + 1) x (N + 3) = (48 +1) (48 +3 ) = 49 x 51 = 2499

Question 14

The average height of the basketball team A is 5 ft 11 inches and that of B is 6 ft 2 inches. There are 20 players in team A and 18 player in team B.The overall average height is

Accepted Answer

Overall height = (n1a1 + n2a2) / (n1 + n2) n1= 20, a1 = 5 ft 11 inches = 5 x 12 + 11 = 71 inches n2= 18, a2 = 6 ft 2 inches = 6 x 12 + 2 = 74 inches ∴ Overall height = [(20) (71) + (18) (74)] / (20+18) = (1420 + 1332) / 38 = 72.42 inches

Question 15

The average of 13 results is 60. If the average of first 7 result is 59 and that of last 7 results is 61, What will be the seventh result?

Accepted Answer

According to the fundamental to the fundamental formula Average(A)= Sum (S) / Number(N) From the question 60 = S / 13 ∴ S = 60 x 13 = 780 Sum of first seven result = 59 x 7 = 413 Sum of last seven result = 61 x 7 = 427 ∴ 7th result = (Sum of first seven result) + (Sum of last seven results) - (Sum of all the results) = (413 + 427 - 780 ) = (840 - 780) = 60 NoteSum of first seven when added to the sum of last seven result, then repetition of 7th result takes place.

Question 16

Average weight of 19 men is 74 kg and the average weight of 38 women is 63 kg. What is the average weight(rounded off to the nearest integer) of all the men and the women together.

Accepted Answer

Here n1 = 19, a1 = 74, n2 = 38, a1 = 63 Total average weight = (n1a1 + n2 a2) / (n1 + n2) = [(19) (74) + (38) (63)] / (19 + 38) = 3800/57 ≈ 67 kg

Question 17

A cricketer had a mean score of 60 runs in 10 innings. Find out how many runs are to be score in the eleventh innings to raise the mean score to 62?

Accepted Answer

Here, n = 10, a = 60, b = 62 Number of runs scored in 11th inning = n (b - a) + b = 10 (62 - 60) + 62 = 20 + 62 = 82

Question 18

The mean weight of 34 students of a school is 42 kg. If the weight of the teacher be included the mean rises by 400g. Find the weight of the teacher?

Accepted Answer

Here n= 34, a = 42 and b = 42.4 Weight of the teacher. = n(b -a) + b = 34 ( 42.4 - 42) + 42.4 = 13.6 + 42.4 = 56.0 kg

Question 19

The average weight of 21 boys was recorded as 64kg. If the weight of the teacher was added, the average increased by one kg. What was the teacher's weight?

Accepted Answer

Here, n = 21, a = 64, b = 65 Weight of teacher = n(b - a) + b = 21( 65 - 64) + 65 = 21 + 65 = 86 kg

Question 20

The average age of 14 girls and their teacher's age is 15 yr. If teacher's age is excluded then the average reduced by 1. What is the teacher's age?

Accepted Answer

Sum of 14 girls and teacher age = 15 x 15 = 225 Without teacher's age sum of 14 girls age = 14 x 14 = 196 ∴ Teacher's age = 225 -196 = 29 year

Average Questions