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# Averages Questions for MAH-CET

Question 1: A group of 20 girls has average age of 12 years. Average of first 12 from the same group is 13 years and what is the average age of other 8 girls in the group?

a) 10

b) 11

c) 11.5

d) Cannot be determined

e) None of these

Solution:

Let the age of each of the girl in the group be $x_1,x_2,x_3,…..,x_{20}$ years

Average age of 20 girls = 12

=> $\frac{(x_1+x_2+x_3+…..+x_{20})}{20}=12$

=> $(x_1+x_2+x_3+…..+x_{20})=12 \times 20=240$ ————(i)

Average of first 12 girls = 13

=> $\frac{(x_1+x_2+x_2+….+x_{12})}{12}=13$

=> $(x_1+x_2+x_3+…..+x_{12})=13 \times 12=156$ ———–(ii)

Subtracting equation (ii) from (i)

=> $(x_1+x_2+x_3+…..+x_{20})$ $-$ $(x_1+x_2+x_3+…..+x_{12}) = (240-156)$

=> $(x_{13}+x_{14}+…..+x_{20})=84$

Dividing above equation by 8

=> $\frac{(x_{13}+x_{14}+……+x_{20})}{8}=\frac{84}{8} = 10.5$

=> Ans – (E)

Question 2: The average of the 5 consecutive even numbers A,B,C,D ,E is 52.what is the product of B & E

a) 2912

b) 2688

c) 3024

d) 2800

e) NONE OF THESE

Solution:

Let the five consecutive even numbers A,B,C,D ,E = $(x-4) , (x-2) , (x) , (x+2) , (x+4)$ respectively.

Average = $\frac{A+B+C+D+E}{5} = 52$

=> $(x-4) + (x-2) + (x) + (x+2) + (x+4) = 52 \times 5$

=> $5x = 52 \times 5$

=> $x = \frac{52 \times 5}{5} = 52$

=> $B = 52 – 2 = 50$ and $E = 52 + 4 = 56$

$\therefore$ Product of B & E = $50 \times 56 = 2800$

Question 3: find the average of set scores? 221,231,441,359,665,525

a) 399

b) 428

c) 407

d) 415

e) None of these

Solution:

Set : 221,231,441,359,665,525

Sum = 221 + 231 + 441 + 359 + 665 + 525 = 2442

=> Required average = $\frac{2442}{6}$

= 407

Question 4: There are three positive numbers, ${1 \over 3}$rd of average of all the three numbers is 8 less than the value of the highest number. Average of the lowest and the second lowest number is 8. Which is the highest number?

a) 11

b) 14

c) 10

d) 9

e) 13

Solution:

Let the three positive numbers be $x,y,z$     (where $x < y < z$)

Average of the three numbers = $\frac{x + y + z}{3}$

Acc. to ques, => $\frac{1}{3} \times (\frac{x + y + z}{3}) = z – 8$

=> $x + y + z = 9z – 72$

=> $x + y = 8z – 72$

Dividing both sides by 2, we get :

=> $\frac{x + y}{2} = 4z – 36$

Also, average of the lowest and the second lowest number is 8, => $\frac{x + y}{2} = 8$

=> $4z – 36 = 8$

=> $4z = 8 + 36 = 44$

=> $z = \frac{44}{4} = 11$

Question 5: The average age of some males and 15 females is 18 years. The sum of the ages of 15 females is 240 years and average age of males is 20 years. Find the number of males.

a) 8

b) 7

c) 10

d) 15

e) None of these

Solution:

Let number of males = $x$

Average age of males = 20 years

=> Sum of age of males = $20 \times x = 20x$ years

Sum of age of females = 240 years

Acc. to ques, => $\frac{(20 x) + (240)}{15 + x} = 18$

=> $20x + 240 = 270 + 18x$

=> $20x – 18x = 2x = 270 – 240 = 30$

=> $x = \frac{30}{2} = 15$

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Question 6: Average score of a class of 50 students, in an exam is 34. Average score of the students who have passed is 52 and the average score of students who have failed is 16. How many students have failed in the exam?

a) 25

b) 20

c) 15

d) 18

e) 30

Solution:

Let the number of students who failed = $x$

=> Number of students who passed = $(50 – x)$

Acc. to ques,

=> $\frac{(52 \times (50 – x)) + (16 \times x)}{50} = 34$

=> $52 \times 50 – 52x + 16x = 34 \times 50$

=> $52x – 16x = 50 \times (52 – 34)$

=> $36x = 50 \times 18$

=> $x = \frac{50 \times 18}{36} = 25$

Question 7: Average score of a class of 50 students, in an exam is 34. Average score of the students who have passed is 52 and the average score of students who have failed is 16. How many students have failed in the exam?

a) 25

b) 20

c) 15

d) 18

e) 30

Solution:

Let the number of students who failed = $x$

=> Number of students who passed = $(50 – x)$

Acc. to ques,

=> $\frac{(52 \times (50 – x)) + (16 \times x)}{50} = 34$

=> $52 \times 50 – 52x + 16x = 34 \times 50$

=> $52x – 16x = 50 \times (52 – 34)$

=> $36x = 50 \times 18$

=> $x = \frac{50 \times 18}{36} = 25$

Question 8: In a class, the average weight of 80 boys is 64 kg and that of 75 girls is 70 kg. After a few days, 60% of the girls and 30% of the boys leave. What would be the new average weight of the class (in kg)? Assume that the average weight of the boys and the girls remain constant throughout.

a) 63

b) 66.09

c) 68.5

d) 65.5

e) 57.5

Solution:

Initially, number of boys = 80 and number of girls = 75

Average weight of boys = 64 kg and average weight of girls = 70 kg

Now, 60% of the girls and 30% of the boys leave

=> Boys left = $\frac{100 – 30}{100} \times 80 = 56$

Girls left = $\frac{100 – 60}{100} \times 75 = 30$

Since, average weight of the boys and the girls remains constant throughout

$\therefore$ New average weight of the class

= $\frac{(56 \times 64) + (30 \times 70)}{56 + 30} = \frac{3584 + 2100}{86}$

= $\frac{5684}{86} = 66.09$ kg

Question 9: In a class, the average weight of 40 boys is 65 kg and that of 50 girls is 60 kg. After a few days, 40% of the girls and 50% of the boys leave. What would be the new average weight of the class (in kg)? Assume that the average weight of the boys and the girls remains constant throughout.

a) 65

b) 62

c) 68

d) 55

e) 58

Solution:

Initially, number of boys = 40 and number of girls = 50

Average weight of boys = 65 kg and average weight of girls = 60 kg

Now, 40% of the girls and 50% of the boys leave

=> Boys left = $\frac{100 – 50}{100} \times 40 = 20$

Girls left = $\frac{100 – 40}{100} \times 50 = 30$

Since, average weight of the boys and the girls remains constant throughout

$\therefore$ New average weight of the class

= $\frac{(20 \times 65) + (30 \times 60)}{20 + 30} = \frac{1300 + 1800}{50}$

= $\frac{3100}{50} = 62$ kg

Question 10: When 9 is subtracted from a two digit number, the number so formed is reverse of the original number. Also, the average of the digits of the original number is 7.5. What is definitely the original number ?

a) 87

b) 92

c) 90

d) 69

e) 96

Solution:

Let the ten’s digit and unit’s digit of the original number be $x$ and $y$ respectively.

=> original number = $10x + y$

Average of digits = $\frac{x + y}{2} = 7.5$

=> $x + y = 7.5 \times 2 = 15$ ————-(i)

When 9 is subtracted from it, => Reverse number = $10y + x$

=> $(10x + y) – 9 = 10y + x$

=> $9x – 9y = 9$

=> $x – y = \frac{9}{9} = 1$ —————-(ii)

Adding equations (i) & (ii), we get :

=> $2x = 16$ => $x = \frac{16}{2} = 8$

Putting it in eqn(i), => $y = 15 – 8 = 7$

$\therefore$ Original number = $87$

Question 11: Average weight of three boys P, T and R is 54 1/3 kgs while the average weight of three boys, T, F and G is 53 kgs. What is the average weight of P, T, R, F and H?

a) 53.8 kgs

b) 52.4 kgs

c) 53.2 kgs

d) Can’t be determined

e) None of these

Solution:

Clearly, there is no information about the weight of H

Thus, we cannot determine their average weights.

Ans – (D)

Question 12: The average age of a man and his son is 48 years. The ratio of their ages is 11 : 5 respectively. What will be ratio of their ages after 6 years ?

a) 6 : 5

b) 5 : 3

c) 4 : 3

d) 2 : 1

e) None of these

Solution:

Let age of man = $11x$ and age of son = $5x$

Sum of ages of man and son = 48 * 2 = 96 years

=> $11x + 5x = 96$

=> $x = \frac{96}{16} = 6$

=> Age of man = 11 * 6 = 66 years

Age of son = 5 * 6 = 30 years

=> Age of man after 6 years = 66 + 6 = 72 years

Age of son after 6 years = 30 + 6 = 36 years

$\therefore$ Required ratio = 72 : 36 = 2 : 1

Question 13: The average age of a man and his son is 18 years. The ratio of their ages is 5 : 1 respectively. What will be the ratio of their ages after 6 years ?

a) 10 : 3

b) 5 : 2

c) 4 : 3

d) 3 : 1

e) None of these

Solution:

Let age of man = $5x$ and age of son = $x$

Sum of ages of man and son = 18 * 2 = 36 years

=> $5x + x = 36$

=> $x = \frac{36}{6} = 6$

=> Age of man = 5 * 6 = 30 years

Age of son = 1 * 6 = 6 years

=> Age of man after 6 years = 30 + 6 = 36 years

Age of son after 6 years = 6 + 6 = 12 years

$\therefore$ Required ratio = 36 : 12 = 3 : 1

Question 14: The average age of a man and his son is 54 years. The ratio of their ages is 23 : 13 respectively. What will be ratio of their ages after 6 years?

a) 10 : 7

b) 5 : 3

c) 4 : 3

d) 3 : 2

e) None of these

Solution:

Let age of man = $23x$ and age of son = $13x$

Sum of ages of man and son = 54 * 2 = 108 years

=> $23x + 13x = 108$

=> $x = \frac{108}{36} = 3$

=> Age of man = 23 * 3 = 69 years

Age of son = 13 * 3 = 39 years

=> Age of man after 6 years = 69 + 6 = 75 years

Age of son after 6 years = 39 + 6 = 45 years

$\therefore$ Required ratio = 75 : 45 = 5 : 3

Question 15: The average of 5 consecutive even numbers A, B, C. D and E is 52. What is the product of B & E?

a) 2916

b) 2988

c) 3000

d) 2800

e) None of these

Solution:

Let the 5 consecutive even numbers be = $(x) , (x+2) , (x+4) , (x+6) , (x+8)$

Sum of these 5 consecutive numbers = 52 * 5 = 260

=> $(x) + (x+2) + (x+4) + (x+6) + (x+8) = 260$

=> $5x = 260 – 20 = 240$

=> $x = 48$

=> B = $x + 2$ = 48 + 2 = 50

E = $x + 8$ = 48 + 8 = 56

$\therefore$ B $\times$ E = 50 * 56 = 2800

Question 16: Find the average of the following set of scores :
221, 231, 441, 359, 665, 525

a) 399

b) 428

c) 407

d) 415

e) None of these

Solution:

Sum of scores = 221 + 231 + 441 + 359 + 665 + 525

= 2442

=> Average score = 2442/6 = 407

Question 17: The average of five positive numbers is 308. The average of first two numbers is 482.5 and the average of last two numbers is 258.5. What is the third number?

a) 224

b) 58

c) 121

d) Cannot be determined

e) None of these

Solution:

Let the numbers be $A_1 , A_2 , A_3 , A_4 , A_5$

=> $A_1 + A_2 + A_3 + A_4 + A_5 = 308 * 5 = 1540$

Also, $A_1 + A_2 = 482.5 * 2 = 965$

and $A_4 + A_5 = 258.5 * 2 = 517$

=> $A_3 = 1540 – 965 – 517 = 58$

Question 18: What will be the average of the following set of scores (Rounded off to the nearest integer) ?
46, 54, 62, 68, 56, 29, 58

a) 45

b) 59

c) 62

d) 48

e) 53

Solution:

Sum of the scores = 46 + 54 + 62 + 68 + 56 + 29 + 58 = 373

=> Required Average = $\frac{373}{7}$

= $53.28 \approx 53$

Question 19: What will be the average of the followings set of scores?
59, 84, 44, 98, 30, 40, 58

a) 62

b) 66

c) 75

d) 52

e) 59

Solution:

Sum of the scores

= 59 + 84 + 44 + 98 + 30 + 40 + 58 = 413

=> Average = $\frac{413}{7}$ = 59

Question 20: The average of five positive numbers is 213. The average of the first two numbers is 233.5 and the average of last two numbers is 271. What is the third number?

a) 64

b) 56

c) 106

d) Cannot be determined

e) None of these

Let the numbers be $A_1 , A_2 , A_3 , A_4 , A_5$
=> $A_1 + A_2 + A_3 + A_4 + A_5 = 213 * 5 = 1065$
Also, $A_1 + A_2 = 233.5 * 2 = 467$
and $A_4 + A_5 = 271 * 2 = 542$
=> $A_3 = 1065 – 467 – 542 = 56$