Averages and alligations level 2

AVERAGES
ALLIGATIONS /
MIXTURES LEVEL 2
C.S.VEERARAGAVAN

Average age of a family of four members is 20. what is the
average age (in years) of the same family of four members
after four years?
1)21 2)24 3) 28 4) 36
If each number is increased / decreased by a certain
quantity n, then the mean also increases or decreases
by the same quantity.
Answer is 24.
12-06-2015
VEERARAGAVAN C S veeraa1729@gmail.com
9894834264
2

The average weight of a class of 40 students is 40 kg. If a
new student, whose weight is 40 kg, joins the class, then
what is the new average weight of the class? 1)40 kg 2)41
kg 3)44 kg 4)80kg.
Total weight of 40 students = 1600 kg.
New average =
1600+40
41
=
1640
41
=40 kg.
Shortcut: If age of new entrant is the old average then there
will be no change in average.
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3

The average age of 2 groups with the same number of
persons is 30 and 40 respectively.
What is the average age of the 2 groups together?
Let the number of persons be x.
Then Total age of both groups are 30x & 40x.
Average age =
30x+40x
2x
=
70x
2x
=35.
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4

In a company the average height of female employees is
160 cm and the average height of male employee is
170cm.
If the total number of employees is 330, what is the
average height of all the employees of the company?
Since the number of female or male is not given, we
cannot determine the average height of all.
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5

The average weight of girls in a class of 50 students is 40
kg. which of the following could be the average weight of
30 of the boys is 50 kg? 1)42 kg 2) 43 kg 3) 45 kg 4) 47
kg?
If there are exactly 30 boys,
GIRLS CLASS BOYS
NUMBER 20 30
AVG WEIGHT 40 50
X
50–X X – 40
50−𝑋
𝑋−40
=
20
30
1500 – 30X = 20X – 800
X =
230
5
= 46
As there are possibly more boys the average will
be greater than 46 but not less
12-06-2015
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6

The average marks scored by girls in a class of 40
students in an examination is 80.
If the number of boys in the class and their average marks
in the same examination are 25 and 72 respectively, what
are the average marks of all the students in the class?
1) 74 2) 75 3) 76 4) 78
Sum of marks of 25 boys = 72 x 25 = 1800
Sum of marks of 15 girls = 80 x 15 = 1200
Average marks of total students =
3000
40
= 75.
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7

In a company, the average salary for female employees is
`.20,000 per month and that of male employees is `.20,000
per month. What is the average salary per month for all
the employees of the company?
1) 19000 2) 20000 3) 21000
4) cannot be determined.
Let number of female be f and male be m.
Average =
20000 𝑚 +20000(𝑓)
𝑚+𝑓
=20000
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8

The average marks scored by Suresh in 5 out of six
subjects is 54. to get an average of 60 in 6 subjects
together, what is the score that Suresh must get in the
sixth subject?
Total marks in 5 subjects = 5x 54 = 270.
Total marks in 6 subjects = 6 x 60 = 360.
Marks in 6th subject should be
= 360 – 270 = 90.
12-06-2015
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9

The ratio of the number of girls to that of boys is 2:3. If the
average weight of girls is 35 kg and that of boys is 40 kg,
what is the average weight of the entire class? (in kg)
1) 36 2) 37 3) 38 4) 39
Number of girls = 2x and boys = 3x.
Sum of age of girls = 70x and boys = 120x
Average age =
190x
5x
= 38.
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10

The average number of chocolates with four is 4.
Another child joins them.
Now, the average number of chocolates with the five children is
5.
What is the number of chocolates with the fifth child?
1) 1 2) 9 3) 5 4) 6
No of chocolates with four = 4x 4 = 16.
Total no after fifth child joined = 5 x 5 = 25.
Number of chocolates with fifth child = 9.
12-06-2015
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11

A bag contains 2 kg of potatoes and 3 kg of tomatoes.
If the cost of potatoes is Rs.5 per kg and that of tomatoes
is Rs.8 per kg, then what is the average price per kilogram
of the vegetables in the bag?
1) Rs.6 2) Rs.6.60 3)Rs.6.80 4)Rs.7
Total cost of potatoes = 10 and tomatoes = 24
Average cost =
10+24
5
= Rs.6.80
12-06-2015
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12

A total of 44 chocolates were distributed among 10 children such that
each girl gets 5 chocolates and each boy gets 4 chocolates. What is the
number of girls?
1) 6 2) 5 3) 4 4) 3
Average chocolates for girls = 5 and boys = 4.
Total average chocolates for the group = 4.4
Using rule of allegation
a
b
=
5−4.4
4.4 −4
=
0.6
0.4
=
3
2
As a+b = 10, a = 6 and b = 4
Hence there are 4 girls.
4 5
4.4
0.6 0.4
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13

The average income of a man for first 9 months is Rs.10,000
per month.
Last 3 months is Rs. 20,000.
Then which of the following is necessarily true regarding the
average income per month for the man?
1) It is between Rs.10,000 and Rs. 15,000.
2) It is exactly Rs.15,000
3) It is between Rs.15,000
Mostly the income was 10000.
Hence average also should be closer to 10000
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14

The average monthly salary of 12 workers and 3 managers in a
factory was Rs. 600.
When one of the manager whose salary was Rs. 720, was replaced
with a new manager, then the average salary of the team went down
to 580.
What is the salary of the new manager?
A. 570 B.420 C.690 D.640
Salary of new person =
Salary of the removed person + No. of members x change in average.
Salary of new person = 720 + (15)(-20)
= 720 – 300
= 420
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15

The average of earnings of a man for
the first four months,
the fifth to the eighth months and
the last four months in a particular year are
Rs.5000 per month, Rs.6000 per month and
Rs.10000 per month respectively.
What is the average salary per month in that year?
1) Rs.6000 2) Rs.7000 3) Rs.8000 4) Rs.9000
Since the period for each of averages is same
Average =
5000+6000+10000
3
=
21000
3
= 7000
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16

QA02 MIXTURES / ALLIGATIONS
C.S.VEERARAGAVAN
veeraa1729@gmail.com
98948 34264

There are 20 litres of a mixture
of water and milk with 30% milk.
How many litres of pure milk have to be added
to the mixture,
so that the ratio of water to milk in the new
solution is 1:1?
1)14 litres 2)6 litres 3)8 litres 4)10 litres
The mixture contains 6 litres milk and 14 litres
water.
Hence 8 litres of milk should be added to get
equal proportion.
12-06-2015
VEERARAGAVAN C S
veeraa1729@gmail.com 9894834264
18

A 16 litre water and milk solution
contains 75% of milk.
How many litres of water is to be added to the
solution such that the percentage of milk in the
new solution is 25%?
1) 28 2) 30 3) 32 4) 24
The solution contains 16 x
3
4
= 12 litres milk and 4
litres water.
If 25% of solution contains 12 litres of milk means
12
25
X75 =36 litres of water is required.
Hence 32 litres of water should be added.
12-06-2015
VEERARAGAVAN C S
19

MIXTURE
Two solutions of sulphuric acid are mixed in the
ratio 1:9. The concentration of sulphuric acid in the
first and second solution are 10% and 20%
respectively. What is the concentration of sulphuric
acid in the new solution?
1) 18% 2) 16% 3) 19% 4) 17%
Let 10 litres of first and 90 litres of second mixed.
Content of sulphuric acid =
10
100
X10+
20
100
X 90
= 19 litres.
Hence the concentrate of sulphuric acid in the new
solution = 19%
12-06-2015
VEERARAGAVAN C S
20

PROFIT ON MIXTURE
A milk man has 10 litres of pure milk.
How many litres of water have to be added to the milk
so that the milk man gets a profit of 150% by selling at
cost price?
1) 25 2) 15 3) 20 4) 30
C.P of 1 litre of mixture =
100
250
𝑋1 =
2
5
Ratio of water and milk is 3:2
Hence 15 litres of water should be
added to get a profit of 150%.
water Mean Price mixture
0 2
5
1
3
5
2
5
12-06-2015
VEERARAGAVAN C S
21

Quantity after replacement
From 10 litre of milk, one litre is taken out and
replaced by one litre of water, then one litre of
solution is taken out and replaced by one litre of
water. What is the content of milk in the solution?
1) 810ml 2)8.1 litre 3) 7.21 litre4) 9 litre
Content of the milk in the solution= x 1−
y
x
n
= 10 1 −
1
10
2
= 8.1 litre
12-06-2015
VEERARAGAVAN C S
22

Quantity after replacement
From 8 litres of pure milk, one litre is taken out and one
litre of water is added.
Again one litre of mixture is taken out and one litre of
water is added.
What is the ratio of milk to water in the final mixture?
1)49:64 2)15:49 3)64:49 4)49:15
Quantity of milk = x 1−
y
x
n
= 8 1−
1
8
2
=
49
8
.
Quantity of water = 8 -
49
8
=
15
8
Hence the ratio is 49: 15
12-06-2015
VEERARAGAVAN C S
23

Mixture – No loss / Gain
6 Kg of sugar costing Rs.15 per kg is added to 9 Kg of sugar costing
Rs.12 per kg.
At what price should this sugar be sold so that there is no loss or
gain?
1)12.50 2)13 3)13.80 4) 14
C.P of 1 Kg of first type = Rs.12
C.P of 1 Kg of second type = Rs.15
Let C.P of 1 Kg of mixture = Rs.x
Given the ratio of mixture = 9:6 = x – 12: 15 – x
135 – 9x = 6x – 72
15x = 207
X = 13.8
The sugar should be sold at Rs.13.80 so that there is no loss or gain.12-06-2015
VEERARAGAVAN C S
24

The average weight of girls in a class of 50
students is 40 kg. which of the following could
be the average weight of 30 of the boys is 50
kg? 1)42 kg 2) 43 kg 3) 45 kg 4) 47 kg?
If there are exactly 30 boys,
GIRLS CLASS BOYS
NUMBER 20 30
AVG WEIGHT 40 50
X
50–X X – 40
50−𝑋
𝑋−40
=
20
30
1500 – 30X = 20X – 800
X =
230
5
= 46
As there are possibly more boys the average
will be greater than 46 but not less
12-06-2015
VEERARAGAVAN C S
9894834264 25

A total of 44 chocolates were distributed among 10 children such
that each girl gets 5 chocolates and each boy gets 4 chocolates.
What is the number of girls?
1) 6 2) 5 3) 4 4) 3
Average chocolates for girls = 5 and boys = 4.
Total average chocolates for the group = 4.4
Using rule of allegation
a
b
=
5−4.4
4.4 −4
=
0.6
0.4
=
3
2
As a+b = 10, a = 6 and b = 4
Hence there are 4 girls.
4 5
4.4
0.6 0.4
12-06-2015
VEERARAGAVAN C S
9894834264 26

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Averages and alligations level 2