averages and alligations level 2
TRANSCRIPT
AVERAGES ALLIGATIONS / MIXTURES LEVEL 2C.S.VEERARAGAVAN
15/04/2023 VEERARAGAVAN C S [email protected] 9894834264
2
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.
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3
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 = =40 kg.
Shortcut: If age of new entrant is the old average then there will be no change in average.
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4
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 = =35.
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5
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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6
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
=1500 – 30X = 20X – 800
X =
As there are possibly more boys the average will be greater than 46 but not less
V
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7
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 = 75.
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8
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
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9
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.
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10
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 = = 38.
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11
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.
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12
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 = Rs.6.80
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13
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
As a+b = 10, a = 6 and b = 4
Hence there are 4 girls.
XIX
4 5
4.4
0.6 0.4
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14
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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15
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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16
The average of earnings of a man forthe 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.9000Since the period for each of averages is sameAverage = = 7000
XX
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 litresThe mixture contains 6 litres milk and 14 litres water. Hence 8 litres of milk should be added to get equal proportion.
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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) 24The solution contains 16 x = 12 litres milk and 4 litres water.If 25% of solution contains 12 litres of milk means =36 litres of water is required.Hence 32 litres of water should be added.
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MIXTURETwo 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 =
= 19 litres.Hence the concentrate of sulphuric acid in the new solution = 19%
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PROFIT ON MIXTUREA 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) 30C.P of 1 litre of mixture = Ratio of water and milk is 3:2Hence 15 litres of water should beadded to get a profit of 150%.
XVI
water Mean Price mixture
0 1
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Quantity after replacementFrom 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 litre 4) 9 litreContent of the milk in the solution=
== 8.1 litre
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Quantity after replacementFrom 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)49:15Quantity of milk =
= = .Quantity of water = 8 - = Hence the ratio is 49: 15
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Mixture – No loss / Gain6 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) 14C.P of 1 Kg of first type = Rs.12C.P of 1 Kg of second type = Rs.15Let C.P of 1 Kg of mixture = Rs.xGiven the ratio of mixture = 9:6 = x – 12: 15 – x135 – 9x = 6x – 72 15x = 207X = 13.8The sugar should be sold at Rs.13.80 so that there is no loss or gain.
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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,
MIXTURE IN AVERAGES
GIRLS CLASS BOYS
NUMBER 20 30
AVG WEIGHT 40 50
X
50–X X – 40
=1500 – 30X = 20X – 800
X =
As there are possibly more boys the average will be greater than 46 but not less
V
15/04/2023
VEERARAGAVAN C S [email protected]
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
As a+b = 10, a = 6 and b = 4
Hence there are 4 girls.
MIXTURE IN AVERAGES XIX
4 5
4.4
0.6 0.4
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