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Arithmetic: Averages Test-5

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Question 1
The average marks obtained by 120 candidates were 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then the number of candidates who passed the examination was
A
100
B
110
C
120
D
150
Question 1 Explanation: 
Total marks achieved by the candidates = 120 x 35 = 4200
The average of passed students = 39
So let the number of passed students = p
Therefore the number of fail students = 120 –p
Now it’s given
4200 = p x 39 +15(120 – p)
From here the value of p = 100
Question 2
3 years ago the average age of a husband, his wife and his son was 27 years and that of his wife and son 5 years ago was 20 yrs .What is the husband’s present age?
A
35 yrs
B
32 yrs
C
40 yrs
D
37 yrs
Question 2 Explanation: 
Let us suppose the present age of the man his wife and his son = a,b,c
Now we are given by the condition that the average age of a husband,
his wife and his son 3 years ago was 27 yrs and that of his wife and son 5 yrs ago was 20 yrs
So {(a – 3) + (b – 3) +(c-3)}/3 = 27
a + b + c = 90…………………………1
And also
{(b-5) + (c – 5)}/2 = 20
b + c = 50 …………………………….2
so from 1 and 2
a =90 – 50 = 40
Question 3
Ten years ago, the ages of the members of a joint family of eight people added up to be 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to?
A
23 years
B
22 years
C
21 years
D
24 years
Question 3 Explanation: 
The total age of all the eight people in the family = 231
As per the information given in the question,
3 years hence the total age of all the people in the family
= 231 + 3 × 8 – 60 + 0 = 195,
Similarly the total age of the people in the family 3 years further later
= 195 + 3 × 8 – 60 + 0 = 159.
Therefore the current average age of all the people in the family
= (159 +32)/8 = 24 years.
Question 4
There are 5 compartments in a train which carries on an average of 10 passengers per compartment. If at least 4 passengers were sitting in each compartment and no compartment have equal number of passengers then maximum how many passengers can be accommodated in any compartment?
A
24
B
28
C
26
D
29
Question 4 Explanation: 
Total number of passengers = 5 x 10 = 50
At least 4 passengers are there in each of the compartment
So in four compartments the number of passengers must be (4 +5 +6 +7 ) = 22
So the number of passengers in the last compartment is 50 – 22 = 28
Question 5
In a hotel, the average expenditure works out to be Rs. 60 per guest for a group 5 guests and Rs. 45 per guest for a group of 10 guests. It is also known that there is fixed expense for a group (which remains the same) irrespective of the number of guests then the average expenditure per guest when there are 15 guests will be?
A
40
B
45
C
60
D
75
Question 5 Explanation: 
Let the fixed expense is Rs a
Let the variable expense is Rs. b
Therefore for 5 guest the total expenditure = a + 5b = 300
Therefore for 10 guest the total expenditure = a + 10b = 450
On calculating b = 30
So the variable cost is 30 per guest and the fixed is 150
For 15 guests the total expenditure 150 + 30 x 15 = 650 and the average = 600/15 = Rs. 40
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