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Arithmetic: Averages Test-6

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Question 1
The average age of a group is increased by 5 years when a person of whose age is 33 yrs was replaced by a person whose age is 58. find the number of persons in the group?
A
4
B
5
C
8
D
9
Question 1 Explanation: 
Increase in the average = 5 years
Replaced person’s age = 33
The age of person who replaced = 58
So the number of persons in the group may be calculated as
New person age = Replaced person + (increase in average x number of terms)
Now we have the values
58 = 33 + (5n)
n = 5
so option b is the right answer
Alternatively
Let the number of members = n
Average = a
Total values will be = na
Now increase in average = 5 years
Therefore total new value = n(a +5)
Now na -33 + 58 = na +5n
na + 25 = na +5n = 5
Question 2
The average height of 30 students is 140 cm .If 4 students whose average height was 90 cm leave the class find the average height of the remaining class
A
148
B
142
C
141
D
150
Question 2 Explanation: 
Average height = 140
Number of students = 30
Therefore total units are = 140 x 30 = 4200
Now the number of students who left the class = 4
And the average height of 4 students = 180
Therefore total units are 90 x 4 = 360  
So the remaining units are 4200 – 360 = 3840 and the remained students are 26 = 148 cm
Question 3
The average of 4 consecutive numbers is A then what will be the average of next 5 numbers of the series
A
4.5
B
3.5
C
4.8
D
5.9
Question 3 Explanation: 
Let the series of the consecutive numbers is x, x+1 , x+2 , x+3.
And the other five numbers would be = , x+4,  x+5,  x+6,  x+7,  x+8,
Now we are given by the average of first 4 numbers i.e. A
So A = {(4x +6)}/4
Therefore A = x + 1.5
Now we asked for the average of 5 next numbers so the next five numbers are
x+4,  x+5,  x+6,  x+7,  x+8, = 5x + 30
let us suppose the average is B
B = 5x + 30 /5 = x +6, which is equal to the A + 4.5
Question 4
The average monthly expenditure of Pranav in the first 7 months of a year is Rs. 3000. What should be his average monthly expenditure over the next months so that his average monthly expenditure over the year is  Rs. 7000
A
13000
B
18500
C
12600
D
16700
Question 4 Explanation: 
Average monthly expenditure of Pranav in the first 7 months of a year = Rs. 3000
So total money would be = 21000
Months left five
Now his average monthly expenditure over the year should be   Rs. 7000
So the total amount would be 7000 x 12 = 84000
So for next five months the salary would be = (84000 – 21000)/5 = 63000/5 = Rs. 12600
Question 5
The average age of 10 students in a class is 15 and if one teacher is added then the average increased by 2years .Find the age of the teacher
A
34
B
25
C
38
D
37
Question 5 Explanation: 
The number of students initially = 10
Average of ages = 15
So the total number of units = 150
Now one teacher is added the number of student and one teacher = 11
And the average is increased by 2 years
So new total units are = 11 x 17 = 187
So the  age of the teacher = 187 – 150 = 37
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