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# Important Average Quantitative questions for Bank, IBPS/SBI PO clerk , Govt and private exams with Tips

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Average question are important in bank/PO exam and also in state Govt Exams, SSC CGL and various private sectors companies written exam. Generally the question asked in Average section are simple if you practice them really hard and use tips and tricks to solve Average questions in short time quickly.

In this article we have briefed you about various important tip and shortcuts to solve average question in Quantitative aptitude. Please go through them one by one and try to practice as many question you can

##### Tricks for Average Problems (Important Formula for Average Questions)
1. Average = Sum of quantities/ Number of quantities
2. Sum of quantities = Average * Number of quantities
3. The average of first n natural numbers is (n +1) / 2
4. The average of the squares of first n natural numbers is (n +1)(2n+1 ) / 6
5. The average of cubes of first n natural numbers is n(n+1)2 / 4
6. The average of first n odd numbers is given by (last odd number +1) / 2
7. The average of first n even numbers is given by (last even number + 2) / 2
8. The average of squares of first n consecutive even numbers is 2(n+1)(2n+1) / 3
9. The average of squares of consecutive even numbers till n is (n+1)(n+2) / 3
10. The average of squares of squares of consecutive odd numbers till n is n(n+2) / 3
11. If the average of n consecutive numbers is m, then the difference between the smallest and the largest number is 2(m-1)
12. If the number of quantities in two groups be n1 and n2 and their average is x and y respectively, the combined average is (n1x+n2y) / (n1+ n2)
13. The average of n quantities is equal to x. When a quantity is removed, the average becomes y. The value of the removed quantity is n(x-y) + y
14. The average of n quantities is equal to x. When a quantity is added, the average becomes y. The value of the new quantity is n(y-x) + y

## Now let’s Practice some average questions from basics :

• Question : A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings?
A. 34
B. 35
C. 36
D. 37

Explanation: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37

• Questions : The average of first 10 natural numbers is?
A. 5
B. 5.5
C. 6
D. 6.5

Explanation: Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5

Question : he average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
A. 9
B. 12
C. 15
D. 18

Explanation: 3x + 5x + 7x = 45
x = 3
3x = 9

Question : The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
A. 6
B. 7
C. 8
D. 9

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Explanation: 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9

Question : A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
A. 625
B. 632
C. 656
D. 665

Explanation: 8 * 84 = 672 – 7 = 665

Question: A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
A. 17
B. 18
C. 19
D. 20

Explanation: Let the average after the 16th inning be P.
So, the average after the 15th inning will be (P-3)
Hence, 15(P-30) + 64 = 16P => P = 19

Quiz on Average Questions for Practice

###### Question : Average of all prime numbers between 30 to 50
1. 37
2. 37.8
3. 39
4. 39.8

Option D

Explanation:

Prime numbers between 30 and 50 are:
31, 37, 41, 43, 47

Average of prime numbers between 30 to 50 will be
\begin{aligned}
(\frac{31+37+41+43+47}{5}) = \frac{199}{5} = 39.8
\end{aligned}

Question : Find the average of first 10 multiples of 7

1. 35.5
2. 37.5
3. 38.5
4. 40.5

Option C

Question :Kritika is on a 4 days trip with school mates. She had decided to keep her average expense for 4 days at Rs 80. However, at the end of third day she realized that her expenses on first three days were Rs 80, Rs 90, Rs 110 and respectively. How much should she spend on 4th day to ensure that she meets her targeted average expense?

a. Rs. 40
b. Rs. 60
c. Rs. 90
d. Rs. 220

∴ 4th day expenditure = Rs. (320 – 280) = Rs 40

Question Find average of natural numbers from 1 to 67?

a. 33.5
b. 34
c. 50
d. 67

b. 34

Explanation:

Tip:

Average of first n even numbers = n+1

Average of first n odd numbers = n

Question : The average weight of 48 students of a class is 36 kg. If the weights of teacher and principle is included. The average becomes 36.76 kg. Find the sum of the weights of teacher and principle?

A. 108 kg

B. 106Kg

C. 118 Kg

D. 110 Kg

Sum of weights of teacher and principle

⇒ New avg. × No. of students – Existing avg. × No. of students

⇒ 36.76 × 50 – 36 × 48 = 1838 – 1728

⇒ 110 kg

∴ Sum of weight of teacher and principle is 110 kg

Questions : The average revenues of 11 consecutive years of a company is Rs. 77 lakhs. If the average of first 6 years is Rs. 72 lakhs and that of last 6 years is Rs. 84 lakhs, What is the revenue for the sixth year.

A. Rs. 89 lakhs

B Rs. 88 lakhs

C Rs. 83 lakhs

D Rs. 84 lakhs

Report

Average revenue for 11 years = Sum of all revenues/11

⇒ 77L = Sum/11

⇒ Sum of revenues for 11 years = 77 × 11 = 847L

Average revenue for first 6 years = Sum of revenues for first 6 years/6

⇒ 72L = Sum of revenues for first 6 years/6

⇒ Sum of revenues of first 6 years = 72 × 6 = 432L

Similarly, Sum of revenues for last 6 years = 84 × 6 = 504L

⇒ Sum of revenues for first 5 years = total sum – sum of revenues of last 6 years

⇒ Sum of revenues for first 5 years = 847 – 504 = 343L

⇒ Revenue in the 6th year = Sum of revenues in first 6 years – sum of revenues in first 5 years

∴ Revenue for 6th year = 432 – 343 = 89 Lakhs

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