Problems on Average with steps set 3

16. There are two divisions A and B of a class, consisting of 36 and 44 students respectively. If the average weight of divisions A is 40 kg and that of division b is 35 kg. What is the average weight of the

whole class?

A. 38.25 B. 37.25 C. 38.5 D. 37

Answer : Option B

Explanation :

Total weight of students in division A = 36×40

Total weight of students in division B = 44×35

Total students = 36+44=80

Average weight of the whole class

= {(36×40)+(44×35)}/80

= {(9×40)+(11×35)}/20

= {(9×8)+(11×7)}/4

= (72+77)/4

= 149/4=37.25

17. A batsman makes a score of 87 runs in the 17th

inning and thus increases his averages by 3. What

is his average after 17th inning?

A. 39 B. 35 C. 42 D. 40.5

Answer : Option A

Explanation :

Let the average after 17 innings = x

Total runs scored in 17 innings = 17x

then average after 16 innings = (x-3)

Total runs scored in 16 innings = 16(x-3)

We know that Total runs scored in 16 innings + 87

= Total runs scored in 17 innings

= > 16(x-3) + 87 = 17x

= > 16x - 48 + 87 = 17x

= > x = 39

18. A student needed 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 is

the value of x?

A. 12 B. 5 C. 7 D. 9

Answer : Option C

Explanation :

(3+11+7+9+15+13+8+19+17+21+14+x)/

12=12

= > (137+x)/12=12

= > 137 + x = 144

= > x = 144 - 137 = 7

19. Arun obtained 76, 65, 82, 67 and 85 marks (out in

100) in English, Mathematics, Chemistry, Biology

and Physics. What is his average mark?

A. 53 B. 54 C. 72 D 75

Answer : Option D

Explanation :

Average mark = (76+65+82+67+85)/

5=375#5=75

20. Distance between two stations A and B is 778

km. A train covers the journey from A to B at 84

km per hour and returns back to A with a uniform

speed of 56km per hour. Find the average speed

of the train during the whole journey?

A. 69.0 km /hr B. 69.2 km /hr C. 67.2 km /hr

D. 67.0 km /hr

Answer : Option C

Explanation :

If a car covers a certain distance at x kmph and

an equal distance at y kmph.

Then,the average speed of the whole journey =

2xy/x+y kmph.By using the same formula, we

can find out the average speed quicklyaverage

speed = 2×84×56# (84+56) =

(2×84×56)#140==67.2

21. The average age of 36 students in a group is 14

years. When teacher’s age is included to it, the

average increases by one. Find out the teacher’s

age in years?

A. 51 years, B. 49 years C. 53 years D. 50 years

Answer : Option A

Explanation :

average age of 36 students in a group is 14

= > Sum of the ages of 36 students = 36×14

When teacher’s age is included to it, the average

increases by one => average = 15

= > Sum of the ages of 36 students and the

teacher =37×15

Hence teachers age =

37×15"36×14=37×15"14(37"1)=37×15"37×14+14=37(15"14)+14=37+14=51

22. The average of five numbers id 27. If one

number is excluded, the average becomes 25.

What is the excluded number?

A. 30, B. 40, C. 32.5, D. 35

Answer : Option D

Explanation :

Sum of 5 numbers = 5×27Sum of 4 numbers

after excluding one number = 4×25Excluded

number = 5×27"4×25=135"100=35

 Problems on Average with steps -Set 2

11. 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. The average age of the family is

A. 32.27 years B. 31.71 years C. 28.17

years D. 30.57 years

Answer : Option B

Explanation :

Total age of the grandparents = 67×2

Total age of the parents = 35×2

Total age of the grandchildren = 6×3

Average age of the family ={

(67×2)+(35×2)+(6×3)}/7=(134+70+18)/

7=222/7=31.71

12. 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, what is the weight of B?

A. 31 kg B. 2812 kg C. 32 kg D. 3012 kg

Answer : Option A

Explanation :

Let the weight of A, B and C are a,b and c

respectively.

Average weight of A,B and C =

a+b+c=45×3=135—equation(1)

average weight of A and B = 40

a+b=40×2=80—equation(2)

average weight of B and C = 43

b+c=43×2=86 —equation (3)

equation(2) +equation(3)- equation(1)

=> a+ b+ b +c “(a +b +c)=80+86”135

=>b=80+86"135=166"135=31

=> weight of B = 31

13. If the average marks of three batches of 55, 60

and 45 students respectively is 50, 55, 60, what

is the average marks of all the students?

A. 53.23 B. 54.68 C. 51.33 D. 50

Answer : Option B

Explanation :

Average marks of batch1 = 50

Students in batch1 = 55

Total marks of batch1=55×50

Average marks of batch2 = 55

Students in batch2 = 60

Total marks of batch2=60×55

Average marks of batch3 = 60

Students in batch3 = 45

Total marks of batch3=45×60

Total students = 55 + 60 + 45 = 160

Average marks of all the students

= {(55×50)+(60×55)+(45×60)}/160

= (275+330+270)/16

= 875/16=54.68

14. 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. 30

Answer : Option A

Explanation :

let the present age of the husband = h

present age of the wife = w

present age of the child = c

3 years ago, average age of husband, wife and

their child = 27

= >Sum of age of husband, wife and their child

before 3 years = 3×27=81

= > (h-3) + (w-3) + (c-3) = 81

= > h + w + c = 81+9 = 90 —————————

equation(1)

5 years ago, average age of wife and child = 20

= >Sum of age of wife and child before 5 years =

2×20=40

= > (w-5) + (c-5) = 40

= > w + c = 40+10 = 50 —————————

equation(2)

Substituting equation(2) in equation(1)

= > h + 50 = 90

= > h = 90 - 50 = 40

= >present age of the husband = 40

15. 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 is the weight of the

new person?

A. 70 B. 75 C. 85 D 80

Answer : Option C

Explanation :

Total increase in weight = 8×2.5=20

If x is the weight of the new person, total

increase in weight = x - 65

=> 20 = x - 65

=> x = 20 + 65 = 85

  Problems on Average with steps : Kerala PSC Degree Level Questions

1. 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. 5.5, C. 7.4 ,D. 5

Answer : Option A

Explanation :

Runs scored in the first 10 overs = 10×3.2=32

Total runs = 282

remaining runs to be scored = 282 - 32 = 250

remaining overs = 40

Run rate needed = 250/40=6.25

2. 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. 4800 B. 4991 C. 5004 D. 5000

Answer : Option B

Explanation : Let the sale in the sixth month = x

Then( 6435+6927+6855+7230+6562+x)/6=6500

= > 6435 + 6927 + 6855+ 7230 + 6562 + x

= 6 × 6500 = 39000

= > 34009 + x = 39000

= > x = 39000 - 34009 = 4991

3. The average of 20 numbers is zero. Of them, How

many of them may be greater than zero, at the

most?

A. 1 B. 20 C. 0 D. 19

Answer : Option D

Explanation : Average of 20 numbers = 0

=>Sum of 20 numbers/20=0

=> Sum of 20 numbers = 0

Hence at the most, there can be 19 positive

numbers.

(Such that if the sum of these 19 positive

numbers is x, 20th number will be -x)

4. 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. Find

out the average age of the team.

A. 23 years B. 20 years C. 24 years D. 21 years

Answer : Option A

Explanation :Number of members in the team = 11

Let the average age of the team = x

=>(Sum of the ages of all the 11 members

of the team)/11=x

=> Sum of the ages of all the 11 members

of the team = 11x

Age of the captain = 26

Age of the wicket keeper = 26 + 3 = 29

Sum of the ages of 9 members of the team

excluding captain and wicket keeper

= 11x - 26 - 29 = 11x - 55

Average age of 9 members of the team

excluding captain and wicket keeper

=(11x”55)/9

Given that( 11x”55)/9=(x”1)

=> 11x - 55 = 9(x - 1)

=> 11x - 55 = 9x - 9

=> 2x = 46

=>x=46/2=23 years

5. The average monthly income of A and B is Rs. 5050.

The average monthly income of B and C is Rs. 6250

and the average monthly income of A and C is Rs.

5200. What is the monthly income of A?

A. 2000 B. 3000 C. 4000 D. 5000

Answer : Option C

Explanation :Let the monthly income of A = a

monthly income of B = b

monthly income of C = a

a +b=2×5050------------(Equation1)

b + c=2×6250------------(Equation2)

a +c=2×5200------------(Equation3)

(Equation 1) + (Equation 3) - (Equation 2)

=> ( a +b +a +c) “ (b +c)

=(2×5050)+(2×5200)”(2×6250)

=> 2a = 2(5050 + 5200 - 6250)

=> a = 4000

=> Monthly income of A = 4000

7. In Kiran’s opinion, his weight is greater than 65 kg

but less than 72 kg. His brother does not agree

with Kiran and he thinks that Kiran’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

Kiran?

 A. 70 kg B. 69 kg C. 61 kg D. 67 kg

Answer : Option D

Explanation : Let Kiran’s weight = x. Then

According to Kiran, 65 < x < 72 ——————

(equation 1)

According to brother, 60 < x < 70 ——————

(equation 2)

According to mother, xd”68 ——————(equation

3) Given that equation 1,equation 2 and equation

3 are correct. By combining these equations,

we can write as

65<xd”68

That is x = 66 or 67 or 68

average of different probable weights of Kiran =

(66+67+68)/3=67

8. 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. 48.55 B. 42.25 C. 50 D. 51.25

Answer : Option A

Explanation :

Average weight of 16 boys = 50.25

Total Weight of 16 boys = 50.25×16

Average weight of remaining 8 boys = 45.15

Total Weight of remaining 8 boys = 45.15×8

Total weight of all boys in the class =

(50.25×16)+(45.15×8)

Total boys = 16+8=24

Average weight of all the boys =

(50.25×16)+(45.15×8)/24

= (50.25×2)+(45.15×1)/3

= (16.75×2) + 15.05

=33.5+15.05=48.55

9. A library has an average of 510 visitors on Sundays

and 240 on other days. What is the average number

of visitors per day in a month of 30 days beginning

with a Sunday?

A. 290 B. 304 C. 285 D. 270

Answer : Option C

Explanation :in a month of 30 days beginning with

a Sunday, there will be 4 complete weeks and

another two days which will be Sunday and Monday

Hence there will be 5 Sundays and 25 other days in

a month of 30 days beginning with

a Sunday

Average visitors on Sundays = 510

Total visitors of 5 Sundays = 510×5

Average visitors on other days = 240

Total visitors of other 25 days = 240×25

Total visitors = (510×5)+(240×25)

Total days= 30

Average number of visitors per day ={ (510×5)

+ (240×25)}/30

= { (51×5)+(24×25) }/3

= (17×5) + (8×25)

=85+200=285

10. A student’s mark was wrongly entered as 83

instead of 63. Due to that the average marks for

the class got increased by half 1/2. What is the

number of students in the class?

A. 45 B. 40 C. 35 D. 30

Answer : Option B

Explanation : Let the total number of students =

x

The average marks increased by 1/2 due to

anincrease of 83-63=20 marks.

But total increase in the marks = 1/2×x=x/2

Hence we can write asx/2=20•Ëx=20×2=40

Kerala PSC Degree Level questions -Set 2

41. The rate of photosynthesis is highest in

..... light:

(a) Yellow (b) Blue

(c) Green (d) Red

42. Wax is soluble in:

(a) Benzene (b) Water

(c) Alcohol (d) Iodine

43. Acid contained in onion:

(a) Oxalic acid (b) Citric acid

(c) Malic acid (d) Prussic acid

44. Element obtained from sea weeds:

(a) Chlorine (b) Calcium

(c) Iodine (d) Magnisium

45. ‘SIM Card’ related to:

(a) Bank (b) Mobile phone

(c) Artificial satellite (d) Black box

46. In which country Three Mile Island

nuclear disaster was occurred in 1979?

(a) USA (b) UK

(c) Ukraine (d) China

47. China was officially declared republic in:

(a) 1912 (b) 1913

(c) 1914 (d) 1915

48. The first country to win the world cup

cricket thrice:

(a) W est Indies (b) Pakistan

(c) England (d) Australia

49. The first team to win Santosh trophy:

(a) Bengal (b) Kerala

(c) Karnataka (d) Tamil Nadu

50. Which is known as the sorrow of

Bengal:

(a) Kosi (b) Damodar

(c) Mahanadi (d) Brahmaputra

51. Which organisation was founded by

Henri Dunant?

(a) Amnesty International

(b) Boy Scouts (c) Lions Club

(d) Red Cross

52. The first to get two booker prizes:

(a) Salman Rushdie (b) Peter Carey

(c) Ben Okri (d) JM Coetzee

53. “We have to now fight for peace with

the same courage and determination as

we fought against aggression”

(a) FD Roosevelt (b) Jawaharlal Nehru

(c) Lal Bahadur Shastri

(d) Indira Gandhi

54. Who wrote ‘Pritvirajaraso’?

(a) Chandbardai (b) Faizi

(c) Tulsidas (d) Surdas

55.Abdul Rahman Tunku was the first prime

minister of:

(a) Malaysia (b) Singapore

(c) Brunei (d) Indonesia

56. Name of which Indus valley site means

‘black bangles’?

(a) Harappa (b) Dholavira

(c) Kalibangan (d) Banawali

57. The founder of Chola empire:

(a) Simhavishnu (b) Vijayalaya

(c) Harihara (d) Simuka

58. Who was the Viceroy when Indian

National Congress was formed in

1885?

(a) Dufferin (b) Reading

(c) Mayo (d) Curzon

59. Whom Gandhiji called ‘the great

sentinel’?

(a) Rajendraprasad

(b) Subhas Chandra Bose

(c) Rabindranath Tagore

(d) Nehru

60. The year of foundation of Muslim

League:

(a) 1903 (b) 1904

(c) 1907 (d) 1906

61. The Indian president who translated

‘The Republic’ of Plato:

(a) VV Giri

(b) Zakkir Hussain

(c) S Radhakrishnan

(d) Rajendraprasad

62. The first to become the prime minister

of India while he/she was a member of

Rajya Sabha:

(a) Lal Bahadur Shastri(b) Indira Gandhi

(c) Rajiv Gandhi (d) PV Narasimha

Rao

Kerala PSC Degree Level questions -Set 2

63. The budget is presented in the Lok

Sabha by the Finance Minister in the

name of the ......of India.

(a) President (b) Prime Minister

(c) RBI Governor (d) Speaker

64. The Winter session of Lok Sabha

begins in the month of:

(a) September (b) October

(c) November (d) December

65. Motions of no confidence against the

government can only be introduced and

passed in the......

(a) Lok Sabha (b) Rajya Sabha

(c) Either House (d) None of these

66. The number of schedules in the

Constitution of India when it was

brought into force:

(a) 12 (b) 10

(c) 9 (d) 8

67. The Indian who headed a new sect ‘The

Order of the Star of the East” at the age

of 20:

(a) Rajaneesh (b) Jiddu

Krishnamurthy (c) Shri Shri

Ravisankar (d) Chinmayananda

68. Kublai Khan was the emperor of:

(a) Russia (b) Egypt

(c) China (d) Persia

69. The nationality of Akiro Kurasova, the

world famous film maker:

(a) France (b) Russia

(c) Japan (d) China

70. Number of members in the first ministry

of Kerala including Chief Minister:

(a) 12 (b) 11

(c) 13 (d) 10

71. In which river Chenkulam hydel project

is built?

(a) Pamba (b) Kallada

(c) Vamaanapuram river

(d) Muthirappuzha

72. ‘The Vrindavan of Kerala’:

(a) Malampuzha Garden

(b) Napier Museum

(c) Neyyar Dam (d) Munnar

73. The taluk in Kerala with the longest

coastline:

(a) Kollam (b) Kozhikode

(c) Cherthala (d) Chirayinkeezhu

74. The annual festival of which temple is

known as ‘Bharani’?

(a) Guruvayur (b) Ambalappuzha

(c) Kodungallur (d) Sabarimala

75.The first Malayali woman to become

Governor of an Indian State:

(a) Fatima Beevi (b) KK Usha

(c)Anna Chandy (d) Mary Punnan

76.The first Indian woman to become grand

master in Chess:

(a) Koneru Humpy(b) Dronavally Harika

(c) Divyendu Barua (d) Saiha Nehwal

77. Chittagong is the main port of:?

(a) Sri Lanka (b) Bangladesh

(c) Maldives (d) Nepal

78. Longest served member of Kerala

Legislative Assembly?

(a) KM Mani (b) GR Gowri

(c) Oommen Chandy (d) PJ Joseph

79. The 193rd member of UNO:

(a) Montenegro (b) South Sudan

(c) Kosovo (d) East Timor

80. The largest Scandinavian country:

(a) Norway (b) Denmark

(c) Sweden (d) None of these

Answers:

 41(d) 42(a) 43(a) 44(c) 45( b) 46(a) 47(a) 48(d) 49(a) 50 (b) 51(d) 52(d) 53(c) 54(a) 55(a) 56(c) 57(b) 58(a) 59(c)60(d) 61(b)62(b) 63 (a) 64(c) 65 (a) 66 (d) 67 (b) 68(c) 69 (c) 70 (b) 71(d) 72(a) 73(c) 74(c)75(a)76(a) 77(b) 78 (a) 79 (b) 80 (c)