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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.
Collapse All
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:
Total number of buses = 30
Total income generated in April 2010 = 0.4 30 20 500 = Rs. 120000
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Total number of buses = 35
Total income generated in April 2010 = 0.8 35 20 300 = Rs. 168000
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.