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1.3 Marks

What is the average score in percentage obtained by Kartik, if he obtained 124 out of

150, 36 out of 50 and 48 out of 75 marks in Science, Geography and History

respectively?

1) 75.36

2) 75.63

3) 72.89

4) 68.88

5) 74.42

Solution:

Hence, option 3.

2.3 Marks

In the year 2009, the average monthly expenditure of a family for the first four months

was Rs. 2840, for the next four months was Rs. 2440 and was Rs. 3440 for the rest of

the year. If they saved Rs. 5060 per month, what was the average income of the family

for the year 2009?

1) Rs. 2996.44

2) Rs. 3154.66

3) Rs. 7211.44

4) Rs. 7866.66

5) Rs. 7966.67

Solution:

The average income of the family for the year 2009

Hence, option 5.

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Section I

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3.3 Marks

The average height of Prakash, Qaiser, and Ronak is 154 cm. Another person

Santosh joins the group and the average height now becomes 162 cm. If another

person Tarun whose height is 10 cm less than that of Santosh, replaces Qaiser then

the average height of the group becomes 145 cm. What is the height of Qaiser?

1) 154 cm

2) 264 cm

3) 174 cm

4) 244 cm

5) 194 cm

Solution:

Let the heights of Prakash, Qaiser, Ronak, Santosh and Tarun bep, q, r, s and t

respectively.

It is given that,

p + q + r= 154 3 = 462 (i)

p + q + r+ s= 162 4 = 648 (ii)

s = 186 cm

It is given that,

t= s 10 = 176 cm

p + r+ s + t= 580

p + r= 580 (186 + 176) = 218 (iii)

Subtracting (iii) from (i),

q = 244

The height of Qaiser = 244 cm

Hence, option 4.

4.3 Marks The average of the number of students in three colleges S, T and U is 845. The

number of students in college S and U is 75 and 81 more than the number of students

in college T. Find the number of students in college T?

1) 845

2) 793

3) 814

4) 781

5) 823

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Solution:

Let the number of students in the colleges S, T and U be s, tand urespectively.

s + t+ u= 845 3 = 2535 (i)

s = 75 + t (ii)

u= 81 + t (iii)

Substituting the value ofs and uin equation (i),

75 + t+ t+ 81 + t= 2535

t= 793

The number of students in college T is 793.

Hence, option 2.

5.3 Marks

The average age of Rahul, Vikas and Sagar, 4 years ago was 42 years and that of

Rahul and Sagar, 7 years ago was 32 years. Find the present age of Vikas.

1) 56 years

2) 58 years

3) 60 years

4) 62 years

5) 64 years

Solution:

Let the present ages of Rahul, Vikas and Sagar bex, yand zyears respectively.

4 years ago,

(x 4) + (y 4) + (z 4) = 42 3 = 126

x+ y+ z= 126 + 12 = 138 (i)

Also, 7 years ago,

(x 7) + (z 7) = 32 2 = 64

x+ z= 64 + 14 = 78 (ii)

Subtracting equation (ii) from (i),

y= 138 78 = 60 years.

So the present age of Vikas is 60 years.

Hence, option 3.

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6.3 Marks

The speed of the Rajdhani Express in going from New Delhi to Howrah station is 90

km/h whereas while coming back from Howrah to New Delhi, its speed is 140 km/h.

Find the average speed of the Rajdhani Express during the whole journey.

1) 105.55 km/h

2) 109.56 km/h

3) 112 km/h

4) 115 km/h

5) 120.57 km/h

Solution:

Let the distance between New Delhi and Howrah be D km.

Hence, option 2.

7.3 Marks

While going to office, Rakesh covers the distance between his house and office in his

car with a speed of 45 km/h but while coming back by the same route, the speed ofthe car reduces by 18 km/h. Find the average speed of the car.

1) 36 km/h

2) 38 km/h

3) 30.5 km/h

4) 33.75 km/h

5) 42.25 km/h

Solution:

Let the distance between Rakeshs office and his house be D km.

Hence, option 4.

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8.3 Marks

The ratio of the present ages of Shyam and Roshan is 3 : 7, whereas their ratio after 2

years will be 1 : 2. Find the average of their ages after 21 years.

1) 21

2) 31

3) 41

4) 25

5) 35

Solution:

The present ages of Shyam and Roshan are 3xand 7xyears respectively.

After 2 years,

6x+ 4 = 7x+ 2

x= 2

So the present ages of Shyam and Roshan are 6 years and 14 years respectively.

Hence, option 2.

9.3 Marks

The current ages of Sangita and Sunita are in the ratio 4 : 11 : 9 years ago, the ratio

of their ages was 1 : 5. Find the average of their ages after 7 years.

1) 14

2) 17

3) 24

4) 32

5) 37

Solution:

The present ages of Sangita and Sunita are 4xand 11xrespectively.

9 years ago,

20x 45 = 11x 9

x= 4

So the resent a es of San ita and Sunita are 16 and 44 ears res ectivel .

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.

Hence, option 5.

10.3 Marks

4 boys appear for a test. The average of the score of the first three boys is 72 while

that of the last three boys is 79. If the last boy scores 96 marks, find the score of thefirst boy.

1) 72

2) 74

3) 87

4) 42

5) 75

Solution:

Let the scores of the four boys be a, b, cand drespectively.

(a + b + c) = 72 3 = 216 (i)

(b + c+ d) = 79 3 = 237 (ii)

d= 96 (iii)

From (ii) and (iii)

b + c= 141 (iv)

From (i) and (iv),

a = 75

Hence, option 5.

11.3 Marks

The average of the points scored by 11 teams in the school cricket tournament is 62.

The average of the points of the first 6 teams is 50 while that of the last six teams is66. Find the points scored by 6th team.

1) 14

2) 28

3) 56

4) 72

5) 96

Solution:

Let the points scored by the 6th team bex.

Total points scored by the 11 teams = 11 62 = 682 (i)

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Total points scored by the first 6 teams = 50 6 = 300

Total points scored by the first 5 teams = 300 x (ii)

Total points scored by the last 6 teams = 66 6 = 396

Total points scored by the last 5 teams = 396 x (iii)

From (i), (ii) and (iii )

300 x+x+ 396 x= 682

696 x= 682

x= 14

Hence, option 1.

12.3 Marks

The average age of a family of 6 members was 52 years, eight years ago. A baby

was born in the family due to which the average age of the family is the same today.

What will be the age of the baby, 10 years hence?

1) 11 years

2) 12 years

3) 14 years

4) 16 years

5) 18 years

Solution:

The total age of the family of 6 members, eight years ago, was = 52 6 = 312

The total age of the family of 6 members today = 312 + (6 8) = 312 + 48 = 360

However, the family has 7 members today.

The total age of the family of 7 members today = 52 7 = 364

The age of the baby = 364 360 = 4 years

10 years hence, age of the baby = 14 years

Hence, option 3.

13.3 Marks

The average daily expenditure of a family in the month of August was Rs. 220. Their

average expenditure, for the first 17 days of the month was Rs. 260 and for the last 15

days was Rs. 180. Find the expenditure of the family on the 17 th day of that month.

1) Rs. 190

2) Rs. 210

3) Rs. 230

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.

5) Rs. 270

Solution:

Let the expenditure of the family on the 17th of August be Rs.x

Total expenditure of the family for the month of August = 220 31 = Rs. 6820

Total expenditure for the first 17 days of August = 260 17 = Rs. 4420

Total expenditure for the first 16 days = Rs. (4420 x)

Total expenditure for the last 15 days of August = 180 15 = Rs. 2700

Total expenditure for the last 14 days = Rs. (2700 x)

4420 x+x+ 2700 x= 6820

x= Rs. 300

Hence, option 4.

14.3 Marks

Regal Travels has buses of type A numbered from A31 to A70, buses of type B

numbered from B24 to B53 and buses of type C numbered from C08 to C42.

Each bus has 20 seats and the cost of each ticket is Rs. 250, Rs. 500 and Rs. 300 for

buses of type A, B and C respectively.

In the month of April, 90% of tickets of buses of type A, 40% of tickets of buses of typeB and 80% of tickets of buses of type C were completely sold.

What is the average income per bus for the month of April?

1) Rs. 4226.65

2) Rs. 4457.14

3) Rs. 4720.72

4) Rs. 6405.05

5) Rs. 6558.17

Solution:

For buses of type A:

Total number of buses = 40

Total income generated in April 2010 = 0.9 40 20 250 = Rs. 180000

For buses of type B:



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Hence, option 2.

15.3 Marks

Simi gifted sweet boxes to her friends Mini, Rimi, Pam, Julie and Joyce. The box

received by Mini was 50 kg in weight. The box received by Joyce was 40% heavierthan the box received by Pam, which was 20% lighter than the box received by Mini.

Rimis box at 80 kg was 25% higher than Julies box. Find the difference in the

average of the three heaviest boxes and the three lightest boxes.

1) 15 kg

2) 18 kg

3) 24.5 kg

4) 10.5 kg

5) 5.5 kg

Solution:

Weight of Minis box = 50 kg

Weight of Pams box = 0.8 50 = 40 kg

Weight of Joyces box = 1.4 40 = 56 kg

Weight of Rimis box = 80 kg

Hence, option 2.

16.3 Marks

Salman covers one third of his journey by car at 35 km/h, the next one third of his

journey by bus at 50 km/h and the rest by bike at 75 km/h. Find his average speedduring the whole journey.

1) 38.46 km/h

2) 44.56 km/h

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3) 48.46 km/h

4) 54.66 km/h

5) 62.25 km/h

Solution:

Let the total distance be 3xkm.

Hence, option 3.

17.3 Marks

A jeweler calculated the weight of a diamond stone 9 times and the average weight

was found to be 2.355 gm. The average weight of the stone after weighing it for the

first four times was 2.854 gm. The weight calculated the fifth time was 0.163 less than

the weight calculated the sixth time, while the average of the last three weights of the

stone was 0.836 gm less than the average of the first four weights. Find the weight of

the diamond obtained by the fifth calculation.

1) 1.781 gm

2) 1.926 gm

3) 2.195 gm

4) 2.331 gm

5) 2.653 gm

Solution:Let the weight of the diamond calculated each time be w1, w2, w3, w4, w5, w6, w7, w8 and

w9 respectively.

As it is given that,

w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9 = 2.355 9 = 21.195 gm (i)

w1 + w2 + w3 + w4 = 2.854 4 = 11.416 gm (ii)

w6 = w5 + 0.163 (iii)

w7 + w8 + w9 = (2.854 0.836) 3 = 6.054 gm (iv)

From i ii iii and iv

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, ,

11.416 + w5 + w5 + 0.163 + 6.054 = 21.195

2w5 = 3.562

w5 = 1.781 gm

Hence, option 1.

Group Question

Answer the following questions based on the information given below.

In Shantivan colony, there are three buildings Rosewood, Pinewood and Teakwood having

40, 50 and 60 members respectively. In the annual sports meet, team Rosewood, team

Pinewood and team Teakwood had an average score of 80, 76 and 76 points

respectively. The highest and lowest points of the teams were as follows:

Now if 10 members are transferred from Pinewood to Rosewood, further, 10 more

members are transferred from Teakwood to Rosewood, and 10 members are transferred

from Rosewood to Pinewood and finally, 10 more are transferred from Teakwood to

Pinewood.

18.3 Marks

What is the maximum possible average achieved by team Rosewood?

1) 78

2) 80

3) 84

4) 86

5) 90

Solution:

Let the teams Rosewood, Pinewood and Teakwood be denoted byR, Pand T

respectively.

10 members from Pand 10 members from Tare transferred to Rand 10

members from Rare transferred to P.

Total number of members inR= 40 + 10 + 10 10 = 50

The maximum possible average for team Rwill be achieved when the transfer

from Pto Ris of ten 80s, from Tto Ris of ten 90s and transfer from Rto Pis

of ten 70s.

Total increase in the points = (10 80) + (10 90) (10 70) = 1000

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Hence, option 3.

19.3 Marks

What is the maximum possible average of team Teakwood?

1) 792) 78

3) 77.5

4) 77

5) 76.5

Solution:

10 members from Tare transferred to Rand 10 members from Tare

transferred to P.

Total number of members in T= 60 10 10 = 40

The maximum possible average for team Twill be achieved when the transfer

from Tto Ris of ten 70s and from Tto Pis of ten 70s.

Decrease in the points = (2 10 70) = 1400

Hence, option 1.

20.3 Marks

The minimum possible value of the average of team Pinewood is:

1) 66.25

2) 70.5

3) 72.5

4) 73.3

5) 60.5

Solution:

10 members from Pare transferred to R, 10 members from Rare transferred to

Pand 10 members from Tare transferred to P.

Total number of members inP= 50 10 + 10 + 10 = 60

The minimum possible average of team Pwill be achieved when transfer from P

to Ris of ten 80s, from Rto Pis of ten 70s and from Tto Pis of ten 70s.

The total increase in the points = (2 10 70) (10 80) = 600

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Hence, option 4.

21.3 Marks

A shopkeeper sold 110 pencils of two different types: type A - pencil with an eraser

attached to it and type B - pencil without an eraser. The cost of the type - A pencil was

Rs. 1.50 more than the cost of the type B pencil. The shopkeeper made Rs. 210 from

the sale of pencils of type - A and Rs. 100 from the sale of pencils of type - B. How

many pencils of each type did the shopkeeper sell and what was the price of eachtype of pencil?

1) 42 pencils with eraser for Rs. 5 and 68 pencils without eraser for Rs. 3.5

2) 70 pencils with eraser for Rs. 3 and 40 pencils without eraser for Rs. 2.5

3) 60 pencils with eraser for Rs. 3.5 and 50 pencils without eraser for Rs. 2

4) Either 1 or 2

5) None of these

Solution:

Let the number of pencils and price of each pencil of type - A be a and Rs. Ca

respectively.

Total amount earned by the shopkeeper from the sales of type - A pencils = Rs. 210

a Ca = 210

Now, the number of pencils of type - B = 110 a

Cost of each pencil of type - B = Ca 1.5

Total amount earned by the shopkeeper from the sales of type - B pencils = Rs. 100

(110 a) (Ca 1.5) = 100

1.5a2 475a + 23100 = 0

a = 256.67 ora = 60

Since the total number of pencils is 110, a = 60

Ca = Rs. 3.5

Number of pencils of type - B = 110 a = 50

Cost of each pencil of type - B = Ca 1.5 = Rs. 2

Hence, option 3.

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22.3 Marks

The average salary of data analysts working in Sterling Infotech is Rs. 5000 while that

of content developers is Rs. 3050. Find the total number of employees in Sterling

Infotech if the average salary of employees is Rs. 3650.

1) 300

2) 240

3) 130

4) 100

5) 80

Solution:

Let the number of data analysts bexand the number of content developers be y.

5000x+ 3050y= 3650(x+ y)

1350x 600y= 0

1350x= 600y

x: y= 600 : 1350

x: y= 4 : 9

Hence only option 3 is possible.

Hence, option 3.

23.3 Marks

Yogeshs annual income for the year 2009 was Rs. 22,000. His average expenditure

for the first 3 months of that year was Rs. 2540. For the next 4 months, his average

monthly expenditure was Rs. 215 less than what it was during the first 3 months. For

the rest of the year, he spent only Rs. 6000. Find the percentage of his annual income

saved in the year 2009.

1) 4.18%

2) 3%

3) 4.18%

4) 1.68%

5) None of these

Solution:

Yogeshs total expenditure in the year 2009

= (2540 3) + ((2540 215) 4) + 6000 = Rs. 22920

Hence, option 3.

24.

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3 Marks, .

correct answer while 2 marks are deducted for every wrong answer. Find the number

of questions he answered correctly.

1) 60

2) 68

3) 72

4) 76

5) 80

Solution:

Let the number of correct answers bex.

The number of wrong answers is 100 x.

Since Sanjay scores 304 marks,

5x 2(100 x) = 304

7x= 504

x= 72

The number of questions answered correctly by Sanjay = 72.

Hence, option 3.

25.3 Marks

The average of the number of marbles owned by 30 boys is 20. If the average of the

number of marbles owned by 10 boys out of these 30 is 30, then find the average of

the number of marbles owned by the remaining boys.

1) 10

2) 25

3) 30

4) 15

5) 20

Solution:

Total number of marbles owned by 30 boys = 20 30 = 600

Total number of marbles owned by 10 boys = 30 10 = 300

Total number of marbles owned by the remaining 20 boys = 600 300 = 300

Average of the number of marbles owned by the remaining 20 boys = 15

Hence, option 4.

26.3 Marks

In 3 hours, a shopkeeper was able to sell 5 books for Rs. 24 each, 8 balls for Rs. 12.5

each, 12 pens for Rs. 15 each and 9 pencils for Rs. 3.5 each. What is the average price

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for one article?

1) Rs. 11

2) Rs. 13

3) Rs. 14.5

4) Rs. 16.5

5) Rs. 19

Solution:

Hence, option 2.27.

3 MarksIn a bag, there are 170 bank notes of Rs. 5, Rs. 10, Rs. 20 denominations. If the total

value of banknotes is Rs. 2300, then which of the following could be the number of

banknotes of Rs. 10?

1) 40

2) 50

3) 70

4) 150

5) None of these

Solution:

Let the number of banknotes of Rs. 5, Rs. 10 and Rs. 20 are a, b and crespectively.

a + b + c= 170 (i)

5a + 10b + 20c= 2300 (ii)

Solving (i) and (ii),

b + 3c= 290 (iii)

Now consider options.

Option 1 is not possible as forb = 40, cis a non-integer.

Option 2 is possible as it satisfies equations (i), (ii) and (iii).

Option 3 is not possible as forb = 70, cis not an integer.

Option 4 is not possible as forb = 140, c= 50 and from equation (i) a becomes

negative.

Hence, option 2.

28.3 Marks

Mrs. Gupta decided to distribute equal number of chocolates amongst her students on

her birthday. However, she later realized that she had counted 5 students less, due to

which each student would now get 5 chocolates less. She then decided to buy 25

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chocolates more so that each student would now get 21 chocolates. What is the total

number of students in her class?

1) 20

2) 25

3) 21

4) 50

5) 52

Solution:

Let the number of students in Mrs. Guptas class bexand the total number of

chocolates be y.

Since she counted 5 students less, actual number of students in her class =x+ 5

From the given data.

5x2 + 25x 5y= 0 (i)

She buys 25 more chocolates, so that each student now gets 21 chocolates.

y= 21x+ 80 (ii)

Substituting (ii) in (i),

5x2 80x 400 = 0

x= 20 orx= 4

Since number of students cannot be negative,x= 20

Actual number of students in Mrs. Guptas class =x+ 5 = 25

Hence, option 2.

29.3 Marks Jayesh travels 6 km in the first quarter of an hour in his car, after which his car breaksdown. He then walks to the bus stop and covers 2 km in the second quarter. The bus

then travels 4 km in the third quarter. Find Jayeshs average speed per hour over the

entire journey. (Assume the entire journey to be continuous without a break in

between)

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1) 4 km/h

2) 48 km/h

3) 26 km/h

4) 18 km/h

5) 16 km/h

Solution:

Hence, option 5.

30.3 Marks

A bus travels 66 km in the first 8 hours of a day, 114 km in the next 8 hours and 28 km

in the next 8 hours. Find the average speed of the bus per day over the entire journey.

1) 69 km/day

2) 17 km/day

3) 58 km/day

4) 208 km/day

5) 125 km/day

Solution:

Hence, option 4.

Group Question

Answer the following questions based on the information given below.

There are 60 students in a class. These students are divided into three groups A, B and C

of 15, 20 and 25 students each. The groups A and C are combined to form group D.

31.3 Marks

What is the average weight of the students in group D?

1) More than the average weight of A.

2) More than the average weight of C.

3) Less than the average weight of C.

4) Indeterminate

Solution:Average weight of group D depends on the average weights of groups A and C.

Thus, nothing can be concluded about the average weight of D.

Hence, option 4.

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32.3 Marks

If one student from Group A is shifted to group B, which of the following will be

true?

1) The average weight of both groups increases.

2) The average weight of both the groups decreases.

3) The average weight of the class remains the same.

4) Cannot be determined.

Solution:

Since the total number of students and the total overall weight of all the students

remain the same, the overall average weight remains the same.

Hence, option 3.

33.3 Marks

If all the students of the class have the same weight, then which of the following

is false?

1) The average weight of all the four groups is the same.

2) The total weight of A and C is twice the total weight of B.

3) The average weight of D is greater than the average weight of A.

4) The average weight of all the groups remains the same even if a

number of students are shifted from one group to another.

Solution:

All the students of the same class have the same weight.

Consider Statement A:

Since all the students have the same weight, the average weight of all the

groups has to be same. Hence, statement 1 is true.

Consider Statement B:

The number of people in group A and C = 15 + 25 = 40, while the number of

people in group B = 20, twice of which is equal to 40.

Hence, statement 2 is true.

Consider Statement C:

Since all students have the same weight, the average weight of D is equal to the

average weight of A.

Hence, statement 3 is false.

Consider Statement D:

Since all students have the same weight, the average weight always remains

the same, even when some students are shifted or removed. Hence, statement

4 is true.

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Hence, option 3.

34.3 Marks

If the mean and median of a set containing 5 natural numbers is 10 and 15

respectively, what can be the maximum value of a number that belongs to the set?

1) 19

2) 18

3) 17

4) 16

Solution:

Sum of the 5 numbers = 5 10 = 50

Since the median is 15, the third number when the numbers are arranged in an

ascending order is 15.

Because we want the 5th number to have the largest possible value, we have tominimize all the other numbers.

The minimum value that the 1st and 2nd number can take is 1.

To minimize the fourth number, it has to be equal to the third number i.e. 15.

The four numbers we now have are 1, 1, 15 and 15. Their total is 32.

So, the fifth number must be equal to 50 32 = 18, which is the largest possible value.

Hence, option 2.

35.3 Marks

If the average of 30 positive and distinct integers is 12410, what is the maximum

possible value any one of the 30 integers can take given that 12381 is the least of the

30 integers?

1) 12975

2) 12445

3) 128454) 12753

5) None of these

Solution:

To find the maximum value of one of the 30 integers, we minimize the remaining 29

integers

As all the integers are positive and distinct, the minimum values that the 29 integers

can have is 12381, 12382, 12383, . . ., 12408, 12409

The sum of the first 29 numbers = 12381 + 12382 + ...+ 12409

= (12380 + 1) + (12380 + 2) + ...+ (12380 + 29)

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= (12380 29) + (1 + 2 + ... + 29)

= 359455

The sum of 30 integers with an average 12410 = 12410 30

= 372300

The maximum value that the 30th integer can take is 372300 359455 = 12845

Hence, option 3.

Note: Another method for calculating 12381 + 12382 + ...+ 12409 is,

12381 + 12382 + ... + 12409 = (12000 29) + (300 19) + (400 10) + (80 9) +

(90 10) + 3 (1 + 2 + ... + 9)

= (12000 29) + (300 19) + (400 10) + (80 9) + (90

10) + (3 45)

But the method given in the solution is quicker.

averages 3

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