Aptitude - Average

In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?

A.  67 Kg

B.  68 Kg

C.  69 Kg

D.  70 Kg

67 Kg

Explanation :

Say, Arun's weight = x

As per Arun his weight is 65 < x < 72

As per his brother, his weight is 60 < x  < 70

As per his mother, his weight is x <= 68 Kgs

The Values satisfying all the above conditions are 66, 67 and 68

So, ( 66 + 67 + 68 ) / 3 = 67

Arun must be weighing 67 Kgs

A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?

A.  Rs. 7.98

B.  Rs. 8.08

C.  Rs. 8.98

D.  Rs. 9.08

Rs. 7.98

Explanation :

Total quantity of petrol consumed in three years is:

( 4000 / 7.5 ) + ( 4000 / 8 ) + ( 4000 / 8.5 )

=> 4000 ( 2/15 + 1/8 + 2/17 ) = 76700 / 51

=> Total amount spent = 3 x 4000 = Rs. 12000/-

=> So, Average Cost = 12000 / (76700/51) = ( 12000 x 51 ) / 76700 = Rs. 7.98/-

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

A.  23 years

B.  24 years

C.  25 years

D.  26 years

23 years

Explanation :

Let the average age of the whole team by x years

=> 11x - ( 26 + 29 ) = 9 ( x - 1 )

=> 11x - 9x = 46

=> 2x = 46

=> x = 23

The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

A.  75 Kgs

B.  75.5 Kgs

C.  85 Kgs

D.  85.5 Kgs

85 Kgs

Explanation :

Average weight is increased by 2.5.

So the new average weight = 8 x 2.5 = 20 Kgs

So weight of new person must be = 65 + 20 = 85 Kgs

A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

A.  28 (4 / 7) years

B.  31 (5 / 7) years

C.  32 (1 / 7) years

D.  35 (5 / 7) years

31 (5 / 7) years

Explanation :

=> Grand Parents -> number = 2, Average age = 67

=> Parents -> number = 2, Average age = 35

=> Grandchildren -> number = 3, Average age = 6

=> Average Age of Family = ( 2 x 67 + 2 x 35 + 3 x 6 ) / ( 2 + 2 + 3 )

=> Average Age of Family = ( 134 + 70 + 18 ) / 7 = 31 (5 / 7) years

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?

A.  6.25

B.  6.5

C.  6.75

D.  7

6.25

Explanation :

Sum  = ( m + n ) x A = 282

m = 10, A(m) = 3.2, n = 40

=> Run Rate for remaining 40 overs = ( ( m + n ) x A  - m A(m) ) / n

=> Remaining run rate = ( 282 - 10 x 3.2 ) / 40 = 250 / 40

=> Remaining run rate = 6.25

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?

A.  Rs. 4991

B.  Rs. 5991

C.  Rs. 6991

D.  Rs. 7991

Rs. 4991

Explanation :

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009

=> Required Sale = [ (6500 x 6) - 34009 ]

=> Rs. 4991

The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

A.  0

B.  1

C.  10

D.  19

19

Explanation :

Average of 20 numbers = 0

=> Sum of 20 numbers = 0 x 20 = 0

It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is -a

The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:

A.  3500

B.  4000

C.  4050

D.  5000

4000

Explanation :

Let P, Q and R represent their respective monthly incomes. Then, we have

P + Q = (5050 x 2) = 10100 .... (i)

Q + R = (6250 x 2) = 12500 .... (ii)

P + R = (5200 x 2) = 10400 .... (iii)

Adding (i), (ii) and (iii), we get:  2(P + Q + R) = 33000  or   P + Q + R = 16500 .... (iv)

Subtracting (ii) from (iv), we get P = 4000

=> P's monthly income = Rs. 4000

The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:

A.  35 years

B.  40 years

C.  45 years

D.  50 years

40 years

Explanation :

Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years

Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years

=> Husband's present age = (90 - 50) years = 40 years

The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

A.  17 kg

B.  20 kg

C.  26 kg

D.  31 kg

31 kg

Explanation :

Let A, B, C represent their respective weights. Then, we have

A + B + C = (45 x 3) = 135 .... (i)

A + B = (40 x 2) = 80 .... (ii)

B + C = (43 x 2) = 86 ....(iii)

Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)

Subtracting (i) from (iv), we get : B = 31

=> B's weight = 31 Kg

The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class

A.  47.55 kg

B.  48 kg

C.  48.55 kg

D.  49 kg

48.55 kg

Explanation :

Required average = [ (50.25 x 16) + (45.15 x 8) ] / ( 16 + 8 )

=> (804 + 361.20) / 24

=> 1165.20 / 24

=> 48.55

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is

A.  270

B.  275

C.  280

D.  285

285

Explanation :

Since the month begins with a Sunday, to there will be five Sundays in the month

Required average = [ (510 x 5) + (240 x 25) ] / 30

=> 8550 / 30

=> 285

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:

A.  53.33

B.  54.68

C.  55.75

D.  56.68

54.68

Explanation :

Required average = [ (55 x 50) + (60 x 55) + (45 x 60) ] / ( 55 + 60 + 45 )

=> (2750 + 3300 + 2700) / 160

=> 8750/160

=> 54.68

A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:

A.  10

B.  20

C.  40

D.  80

40

Explanation :

Let there be z pupils in the class

Total increase in marks = ( z x 1/2) = z/2

=> z/2 = (83-63) => z/2 = 20

=> z = 40

A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ?

A.  3

B.  7

C.  17

D.  31

7

Explanation :
No Explanation available for this question

There are two examination rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is;

A.  20

B.  80

C.  100

D.  200

100

Explanation :
No Explanation available for this question

Rahim buys 3 kg mangoes for Rs 21 and sells them at 5 kg for Rs 50. To earn Rs 102 as profit, the mangoes to be sold by him should be

A.  34 kg

B.  52 kg

C.  26 kg

D.  32 kg

34 kg

Explanation :
No Explanation available for this question

The average of 10 numbers is 40.2. Later it is found that two  numbers have been wrongly copied. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.

A.  40.1

B.  40.4

C.  40.6

D.  40.8.

E.  None of the above

40.1

Explanation :
No Explanation available for this question

16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of groups B?

A.  77 1/3

B.  77 2/3

C.  78 1/3

D.  78 2/3

77 2/3

Explanation :
No Explanation available for this question

When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must the plot be sold in order to gain 15% ?

A.  Rs. 21, 000

B.  Rs. 22,500

C.  Rs. 25, 300

D.  Rs. 25,800

Rs. 25, 300

Explanation :
No Explanation available for this question

The average number of printing error per page in a'bod 512 pages is 4. If the total number of printing error ml first 302 pages is 1,208, the average number of printinget per page in the remaining pages is'

A.  0

B.  4

C.  840

D.  90

E.  None of the above

4

Explanation :
No Explanation available for this question

If he is able to sell only 1200 out of the 1500 watches he has made in the season, then in the season he has made a profit of:

A.  Rs. 90,000

B.  Rs. 75,000

C.  Rs. 45,000

D.  Rs. 60,000

Rs. 45,000

Explanation :
No Explanation available for this question

Find the average of the following set of scores.746 1020 321 12 63 428 226 144

A.  367.5

B.  370

C.  360

D.  368.75

E.  None of these

370

Explanation :
No Explanation available for this question

A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is:

A.  10

B.  20

C.  40

D.  73

E.  None of the above

40

Explanation :
No Explanation available for this question

A trader marked the price of his commodity so as to include a profit of 25%. He allowed discount of 16% on the marked price. His actual profit was;

A.  5%

B.  9%

C.  16%

D.  25%

5%

Explanation :
No Explanation available for this question

The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?

A.  40

B.  32

C.  28

D.  26

40

Explanation :
No Explanation available for this question

The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is:

A.  35.2

B.  36.1

C.  36.5

D.  39.1

36.5

Explanation :
No Explanation available for this question

The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then :

A.  x = y + z

B.  2x = y + z

C.  x = 2y + 2z

D.  none of these

2x = y + z

Explanation :
No Explanation available for this question

There are three classes X,Y and Z. Average of class X is 83. Average of Class Y is 76. Average of class Z is 85. Average of class X and Y is 79, average of class Y and Z is 81. Find average of three Classes

A.  81

B.  81.5

C.  82

D.  84