AAO Exam-CT 11: Quant (Average)

AAO Exam-CT 11- Quant (Average)

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AAO Exam-CT 11: Quant (Average)
1. In an exam, the average marks of 40 students is 75. Afterwards, it is found that the marks of 2 students are taken wrong as 56 and 38 instead of 65 and 69. Find the correct average.
  • 74
  • 72
  • 76
  • 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 

2. The average of four numbers equals 25. If one of the numbers is eliminated, the remaining number's average is 20. What was the number that was removed?
  • 60
  • 40
  • 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.

  • 1020
  • 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

4. Monthly savings of A is Rs. 6000 more than that of B. Monthly salaries of A and B are in the ratio 16 : 11. Find the average monthly salary of both of them together, if the monthly expenditure of A is one-third more than the expenditure of B and A saves Rs. 12000 in a month.
  • Rs. 39000
  • Rs. 39500
  • Rs. 40000
  • Rs. 40500
  • 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

5. Sachin's batting average for 50 innings is 60 runs. His highest score exceeds his lowest score by 182 runs. If these two innings are excluded, the average of the remaining 48 innings is 58 runs. The lowest score made by Sachin in his inning is: 
  • 16
  • 17
  • 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.

6. Average number of books read by Ankur in 3 days (Monday, Tuesday, and Wednesday) is 20. On Monday he read 10 more books than that on Tuesday. On Wednesday he read 10 books less than that on Tuesday. Find the number of books read on each day.
  • 30, 20 and 10
  • 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

7. A girl aged 20 years left the class and in place of her a new boy joined the class. If the average of the class has decreased by 6 months, find the age of the new boy who joined the class if the total number of students in the class is 28.
  • 4 years
  • 5 years
  • 6 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

8. The age of 4 friends Aditya, Sabir, Amit and Shivam is 26 years, 25 years, 24 years and 22 years respectively. Find the average age of all of them.
  • 22.75 years
  • 23.5 years
  • 24.25 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

9. The average of length and breadth of the rectangle is 15 cm. The average of breadth and side of a square are 11 cm. The average area of a square and a rectangle is 158 sq.cm. The difference between the breadth of the rectangle and side of a square is 2cm. What is the perimeter of a rectangle?
  • 35 cm
  • 40 cm
  • 30 cm
  • 60 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 + M2 = 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

10. There are 18 books in a library which average cost is Rs. 9000. Out of which 3 books A, B and C are taken out in which A’s price is 25% more than B and C’s price is 25% less than B. Find the price of A if the average of remaining books is Rs. 7000.
  • Rs. 20,375
  • Rs. 21,225
  • Rs. 23,340
  • Rs. 21,830
  • Rs. 23,750

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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