AAO ExamCT 11: Quant (Average)
AAO ExamCT 11 Quant (Average)

74

72

80

None of these
Given
Average marks of 40 student = 75
Formula Used
Average = Sum of observation/No. of observation
Calculation
Total marks of 40 student = 75 × 40 = 3000
Difference in marks of 2 student = (65  56) + (69  38) = 40
So, new total marks of 40 student = 3000 + 40 = 3040
Average = 3040/40 = 76 marks
∴ The correct average of 40 student is 76 marks

60

50

25

30
Given:
The average of four numbers = 25
Calculation:
The average of four numbers = 25
⇒ Sum of the four numbers = 25 × 4 = 100
Average of remaining 3 numbers = 20
⇒ Sum of remaining 3 numbers = 20 × 3 = 60
The number removed = 100  60 = 40
∴ The number removed is 40.
3. In a bank the average salary of all the Staff is Rs. 600. The average salary of all 12 officers is Rs. 4000 and the average salary of the rest Staff is Rs. 560. Find the number of rest of the staff in the bank.

1000

1100

1120

None of these
Given
The average salary of all the Staff in a bank = Rs. 600
The average salary of all 12 officers = Rs. 4000
The average salary of the rest Staff = Rs. 560
Formula Used
Average = Sum of observation/No. of observation
Calculation
Let the number of rest of the staff in the Bank = x
Total salary of rest of staff members in the bank = Rs. 560x
Total salary of 12 officers = 12 × 4000 = Rs. 48000
Total salary of all the staff of the bank = 600 (12 + x)
⇒ 48000 + 560x = 600 (12 + x)
⇒ 48000 + 560x = 7200 + 600x
⇒ 600x  560x = 40800
⇒ 40x = 40800
⇒ x = 1020
∴ The number of rest of the staff in the Bank is 1020

Rs. 39000

Rs. 39500

Rs. 40000

Rs. 41000
Given:
Salary ratio = 16 : 11
A's expenditure = 4/3 of B's expenditure
A's savings = 6000 + B's savings
A's savings = Rs. 12000
Calculation:
Let expenditure of B be Rs. x
A's expenditure = 4x/3
B's savings = 12000  6000 = 6000
A.T.Q
(4x/3 + 12000)/(x + 6000) = 16/11
⇒ 44x/3 + 132000 = 16x + 96000
⇒ 4x/3 = 36000
⇒ x = Rs. 27000
B's salary = 27000 + 6000 = 33000
A's salary = 4/3 × 27000 + 12000 = Rs. 48000
Average salary = (33000 + 48000)/2 = Rs. 40500
∴ The average salary is Rs. 40500

16

18

29

None of these
Given
Average of 50 innings = 60 runs
Formula Used
Average = sum of data/ No. of data
Calculation
So, the sum of 50 innings runs = 60 × 50 = 3000
Let the highest score of the innings = x
and the score of lowest innings = y
then, x – y = 182 runs (1)
According to the question
when these two innings are excluded, the average of the remaining 48 innings = 58 runs
so, the sum of 48 innings runs = 58 × 48 = 2784
⇒ x + y = 3000 – 2784 = 216 runs
Now, x + y = 216 (2)
By solving both the eq , we get x = 199 runs and y = 17 runs
∴ The lowest score is 17 runs.

10, 20 and 40

20, 20 and 20

40, 10 and 10

15, 15 and 30
Given:
Average books read in 3 days = 20
Formula used:
Average = (sum of all observation) / total number of observation
Calculation:
Total number of books read = 20 × 3 = 60
Let the number of books read on Tuesday be x
⇒ Books read on Monday = x + 10
⇒ Books read on Wednesday = x  10
According to question:
x + 10 + x + x  10 = 60
⇒ 3x = 60
⇒ x = 20
∴ Books read on Monday = 20 + 10 = 30
Books read on Tuesday = 20
Books read on Wednesday = 20  10 = 10

4 years

5 years

7 years

8 years
Given:
Total number of students in the class = 28
Age of girl who left the class = 20 years
Average of the class decreased by 6 months
Formula used:
Average = Sum of Terms/Number of terms
Calculation:
Let the sum of the age of 28 students be x
Average of 28 students = x/28
Now, a girl of 20 years left the class and a new boy joined
Age of new boy be y
Sum of 28 students = x – 20 + y
New average of 28 students = (x – 20 + y)/28
Now, x/28 – (x – 20 + y)/28 = 6 months
⇒ (x/28) – (x – 20 + y)/28 = 1/2 year
⇒ (x – x + 20 – y)/28 = 1/2 year
⇒ (20 – y) = 14 years
⇒ y = 6 years
∴ Age of new boy is 6 years
Alternate Solution:
Total number of students in the class = 28
Average decreased by 6 months or 1/2 year
Age of girl who left = 20 years
Age of boy who joined = (20 – (28 × 0.5)
⇒ (20 – 14) years
⇒ 6 years
∴ Age of new boy is 6 years

22.75 years

23.5 years

25.25 years

23.75 years
Given:
Age of Aditya = 26 years
Age of Sabir = 25 years
Age of Amit = 24 years
Age of Shivam = 22 years
Formula used:
Average = Sum of Terms/Number of Terms
Calculation:
Sum of ages of 4 friends = (26 + 25 + 24 + 22) years
⇒ 97 years
Number of friends = 4
Average age = (97/4) years
⇒ 24.25 years ∴ The average age of 4 friends is 24.25 years

35 cm

40 cm

30 cm

45 cm
Given:
Let the length and breadth of the rectangle be A cm and B cm respectively.
⇒ A + B = 30
Formula:
Average area = total area / number of figures
Calculation:
Let the side of a square be M cm.
⇒ B + M = 22
⇒ B – M = 2
Solving,
B = 12cm and M = 10cm
Then,
⇒ A × B + M^{2} = 316
⇒ A × 12 + 100 = 316
⇒ 12A = 216
⇒ A = 18 cm
Perimeter of a rectangle = 2(A + B)
= 2(12 + 18) Perimeter of a rectangle = 60 cm

Rs. 20,375

Rs. 21,225

Rs. 23,340

Rs. 21,830
Given:
Average of 18 books = Rs. 9000
Price of A = 25% more than B
Price of C = 25% less than B
Average of remaining books = Rs. 7000
Concept used:
Total price of books = Number of books × Average price of books
Calculation:
Let the price of B = 100x
Then price of A will be 125x
And price of C will be 75x
Total price of A, B and C = 100x + 125x + 75x
⇒ 300x
Now, Average price of 18 books = Rs. 9000
Total price of 18 books = Rs. 9000 × 18
⇒ Rs. 162,000
Now, average price of 15 books = Rs. 7000
⇒ Rs. 105,000
Now, Total price of 18 books will be equal to total price of 15 books + Total price of A, B and C
⇒ 162,000 = 105,000 + 300X
⇒ 300x = 57,000
⇒ x = 190
Now, price of A = 125x
⇒ Rs. (125 × 190)
∴ The price of A is Rs. 23,750
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