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__Average Aptitude Problems with Solutions: Set 01__

__Average Aptitude Problems with Solutions: Set 01__

__Question No. 01__
The average
age of 30 boys of a class is equal to 14 years. When the age of the class teacher
is included the average becomes 15 years. Find the age of the class teacher.

(A) 30 years

(B) 35 years

(C) 45 years

(D) 52 years

Answer:
Option C

__Explanation:__
Total age of
30 boys = 14 × 30 = 420 years

Total age
when the teacher is included = 15 × 31 = 465 years

∴ Age
of the class teacher = 465 - 420 = 45 years

**Alternate Method: Direct Formula**

Age of new
entrant = New average + (No. of old members × change in average)

= 15 + 30 (15
- 14) = 45 years.

__Question No. 02__
The captain
of a cricket team of 11 members is 26 years old and the wicket keeper is 3
years older. If the ages of these two are excluded, the average age of the
remaining players is one year less than the average age of the whole team. What
is the average age of the team?

(A) 23 years

(B) 24 years

(C) 25 years

(D) None of
these

Answer:
Option A

__Explanation:__
Let the
average age of the whole team by

*x*years.
∴ 11

*x*- (26 + 29) = 9(*x*-1)
=> 11

*x*- 9*x*= 46
=> 2

*x*= 46
=>

*x*= 23.
So, average
age of the team is 23 years.

__Question No. 03__
The average
age of boys in the class is twice the number of girls in the class. If the
ratio of boys and girls in the class of 36 be 5 : 1, what is the total of the
ages (in years) of the boys in the class?

(A) 380

(B) 342

(C) 372

(D) 360

Answer:
Option D

__Explanation:__
Number of
boys = (36 ×

^{5}/_{6}) = 30 years
Numbers of
girls = 6

Average age
of boys = (2 × 6) = 12 years

Total age of
boys = (30 × 12) years = 360 years.

__Question No. 04__
A car owner
buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive
years. What approximately is the average cost per litre of petrol if he spends
Rs. 4000 each year?

(A) Rs. 7.98

(B) Rs. 8

(C) Rs. 8.50

(D) Rs. 9

Answer:
Option A

__Explanation:__
Total
quantity of petrol consumed in 3 years

= {(4000/7.50)
+ (4000/8) + (4000/8.50)} litres

= 4000 {(2/15)
+ (1/8) + (2/17)} litres

= (76,700/51)
litres

Total amount
spent = Rs. (3 × 4000) = Rs. 12,000

∴ Average
cost = Rs. (12,000 × 51)/ 76,700

= Rs. 6120/767

= Rs. 7.98

__Question No. 05__
In Ankit's
opinion, his weight is greater than 65 kg but less than 72 kg. His sister does
not agree with Ankit and she thinks that Ankit's weight is greater than 60 kg
but less than 70 kg. His mother's view is that his weight cannot be greater
than 68 kg. If all are them are correct in their estimation, what is the
average of different probable weights of Ankit?

(A) 67 kg.

(B) 68 kg.

(C) 69 kg.

(D) None of
these

Answer:
Option A

__Explanation:__
Let Ankit's
weight be

*x*kg.
According to
Ankit, 65 <

*x*< 72
According to
Ankit's sister, 60 <

*x*< 70
According to
Ankit's mother,

*x*≤ 68
The values
satisfying all the above conditions are 66, 67 and 68.

∴ Required
average = (66 + 67 + 68)/3 = 201/3 = 67 kg.

__Question No. 06__
Indian
shooting team of 8 persons joins in a shooting competition. One of them scored
85 points. If he had scored 92 points, the average score for the team would
have been 84. The numbers of points, the team scored was

(A) 672

(B) 665

(C) 645

(D) 588

Answer:
Option B

__Explanation:__
Let the
total score be x.

Therefore, (

*x*+ 92 - 85)/8 = 84
=> (

*x*+ 7) = 672
=>

*x*= 665

__Question No. 07__
If the
average marks of three batches of 55, 60 and 45 students respectively is 50,
55, 60, then the average marks of all the students is:

(A) 53.33

(B) 54.68

(C) 55

(D) None of
these

Answer:
Option B

__Explanation:__
Required
average = {(55 × 50) + (60 × 55) + (45 × 60)} / (55 + 60 + 45)

= (2750 + 3300
+ 2700)/160

= 8750/160

= 54.68

__Question No. 08__
Three years
ago, the average age of Raju, Ranjan and Ravi was 27 years and that of Ranjan
and Ravi, 5 years ago was 20 years. Raju’s present age is

(A) 30 years

(B) 35 years

(C) 40 years

(D) 48 years

Answer:
Option C

__Explanation:__
Present age
of (Raju + Ranjan + Ravi) = {(27 × 3) + (3 × 3)} = 90 years.

Present age
of (Ranjan + Ravi) = {(20 × 2) + (2 × 5)} = 50 years.

Therefore,
Raju’s present age = (90 - 50) = 40 years.

__Question No. 09__
The average
monthly income of ‘P’ and ‘Q’ is Rs. 5050. The average monthly income of ‘Q’
and ‘R’ is Rs. 6250 and the average monthly income of ‘P’ and ‘R’ is Rs. 5200.
The monthly income of ‘P’ is:

(A) 3500

(B) 4000

(C) 4050

(D) 5000

Answer:
Option B

__Explanation:__
Let

*P*,*Q*and*R*represent their respective monthly incomes. Then, we have:*P*+

*Q*= (5050 × 2) = 10,100 …..... (i)

*Q*+

*R*= (6250 × 2) = 12,500 …….. (ii)

*P*+

*R*= (5200 × 2) = 10,400 …….. (iii)

Adding (i),
(ii) and (iii), we get: 2(

*P*+*Q*+*R*) = 33,000 or*P*+*Q*+*R*= 16,500 …..... (iv)
Subtracting
(ii) from (iv), we get

*P*= 4000.
∴

*P*'s monthly income = Rs. 4000

__Question No. 10__
The average
of 5 consecutive numbers is ‘

*n*’. If the next two numbers are also included, the average will
(A) Increase
by 1

(B) Remain
same

(C) Increase
by 1.4

(D) Increase
by 2

Answer:
Option A

__Explanation:__
Let, 5
consecutive numbers be, x, x+1, x+2, x+3 and x+4

Their
average is = (5x + 10)/5 = (x + 2)

The next two
numbers are = (x + 5) and (x + 6)

Therefore,
Average of the numbers = [(5x + 10) + (x + 5) + (x + 6)]/7 = (7x + 21)/7 = (x
+3)

So, the
average increased by 1.

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