What is Average? / औसत क्या है?

Average represents the central value of a group of quantities.

औसत किसी समूह की राशियों का एक प्रतिनिधि या केंद्रीय मान होता है।

Formula / सूत्र

Average = Sum of observations ÷ Number of observations

औसत = सभी पदों का योग ÷ पदों की संख्या

Therefore:

Sum = Average × Number

योग = औसत × संख्या

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Example / उदाहरण

Find the average of:

10, 20, 30, 40, 50

Sum = 150

Number of terms = 5

Average = 150÷5

= 30

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Important Concept 1 — Consecutive Numbers

महत्वपूर्ण अवधारणा 1 — क्रमागत संख्याएँ

For consecutive numbers arranged symmetrically, the average is the middle number.

सममित रूप से क्रमागत संख्याओं का औसत बीच की संख्या होती है।

Example:

11, 12, 13, 14, 15

Average = 13

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Consecutive Odd Numbers / क्रमागत विषम संख्याएँ

3, 5, 7, 9, 11

Average = 7

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Consecutive Even Numbers / क्रमागत सम संख्याएँ

12, 14, 16, 18, 20

Average = 16

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Average of First n Natural Numbers

प्रथम n प्राकृतिक संख्याओं का औसत

Numbers:

1,2,3,...n

Average:

(n+1)/2

Example:

First 20 natural numbers:

Average = (20+1)/2

= 10.5

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Average of First n Odd Numbers

प्रथम n विषम संख्याओं का औसत

The first n odd numbers are:

1,3,5,...,(2n−1)

Average = n

Example:

First 15 odd numbers:

Average = 15

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Average of First n Even Numbers

प्रथम n सम संख्याओं का औसत

2,4,6,...,2n

Average = n+1

Example:

First 20 even numbers:

Average = 21

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Adding a New Number / नई संख्या जोड़ना

If average of n numbers is A:

यदि n संख्याओं का औसत A है:

Total = nA

If a new number x is added:

नई संख्या x जोड़ने पर:

New Average:

(nA+x)/(n+1)

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Removing a Number / संख्या हटाना

If one number x is removed:

यदि x को हटाया जाए:

New average:

(nA−x)/(n−1)

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Replacing a Number / संख्या बदलना

If a number x is replaced by y:

यदि x की जगह y आए:

Change in total:

y−x

Therefore:

Change in average = (y−x)/n

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Average Speed / औसत चाल

Average speed is:

Total distance / Total time

औसत चाल निकालते समय सीधे दो चालों का औसत लेना हमेशा सही नहीं होता।

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Equal Distances / समान दूरी

If a person travels equal distances at speeds x and y:

यदि समान दूरी x और y चाल से तय की जाए:

Average Speed = 2xy/(x+y)

Example:

60 km/h and 40 km/h

= (2×60×40)/(100)

= 48 km/h

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Average Practice — 30 Questions

औसत अभ्यास — 30 प्रश्न

Q1

Find the average of 10, 20, 30, 40 and 50.
10, 20, 30, 40 और 50 का औसत ज्ञात करें।

A. 25
B. 30
C. 35
D. 40

Answer / उत्तर: B

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Q2

Average of 15, 25, 35, 45 is:

A. 25
B. 30
C. 35
D. 40

Answer / उत्तर: B

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Q3

Average of 11, 12, 13, 14, 15 is:

A. 12
B. 13
C. 14
D. 15

Answer / उत्तर: B

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Q4

Average of first 20 natural numbers is:

A. 10
B. 10.5
C. 11
D. 20

Answer / उत्तर: B

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Q5

Average of first 25 odd numbers is:

A. 12.5
B. 24
C. 25
D. 50

Answer / उत्तर: C

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Q6

Average of first 30 even numbers is:

A. 30
B. 31
C. 32
D. 60

Answer / उत्तर: B

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Q7

Average of 8 numbers is 25. Their sum is:

A. 175
B. 180
C. 200
D. 225

Answer / उत्तर: C

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Q8

Average of 12 numbers is 18. Sum is:

A. 196
B. 206
C. 216
D. 226

Answer / उत्तर: C

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Q9

Average of five numbers is 24. If four numbers total 86, find the fifth number.

A. 30
B. 32
C. 34
D. 36

Answer / उत्तर: C

Explanation / व्याख्या: Total=5×24=120. Fifth=120−86=34. / कुल 120, अतः पाँचवीं संख्या 34।

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Q10

Average of 10 numbers is 40. If one more number 51 is added, new average is:

A. 40
B. 41
C. 42
D. 45

Answer / उत्तर: B

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Q11

Average age of 20 students is 15 years. A teacher joins and average becomes 16. Teacher's age is:

A. 32
B. 34
C. 36
D. 40

Answer / उत्तर: C

Explanation / व्याख्या: Old total=300. New total=21×16=336. Teacher=36.

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Q12

Average of 6 numbers is 20. If one number 25 is removed, sum of remaining numbers is:

A. 90
B. 95
C. 100
D. 105

Answer / उत्तर: B

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Q13

Average of 15 numbers is 30. One number 40 is replaced by 70. New average is:

A. 31
B. 32
C. 33
D. 35

Answer / उत्तर: B

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Q14

Average marks of 30 students is 60. If one student's marks were wrongly taken as 70 instead of 40, correct average is:

A. 58
B. 59
C. 60
D. 61

Answer / उत्तर: B

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Q15

Average of 7 consecutive integers is 35. Largest number is:

A. 36
B. 37
C. 38
D. 39

Answer / उत्तर: C

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Q16

Average of 9 consecutive odd numbers is 27. Largest number is:

A. 33
B. 35
C. 37
D. 39

Answer / उत्तर: B

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Q17

Average of five consecutive even numbers is 32. Smallest number is:

A. 26
B. 28
C. 30
D. 32

Answer / उत्तर: B

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Q18

Average of A and B is 25. Average of B and C is 30. If A=20, find C.

A. 30
B. 35
C. 40
D. 45

Answer / उत्तर: C

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Q19

Average of 40 students is 50. Average of 20 of them is 60. Average of remaining 20 is:

A. 35
B. 40
C. 45
D. 50

Answer / उत्तर: B

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Q20

Average salary of 10 workers is ₹20,000. If manager's salary is also included, average of 11 persons becomes ₹25,000. Manager's salary is:

A. ₹50,000
B. ₹60,000
C. ₹75,000
D. ₹80,000

Answer / उत्तर: C

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Q21

Average weight of 8 persons increases by 2 kg when a 60-kg person is replaced. Weight of new person is:

A. 72 kg
B. 74 kg
C. 76 kg
D. 80 kg

Answer / उत्तर: C

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Q22

The average of 13 numbers is 48. If average of first 7 is 42 and last 7 is 54, the common number is:

A. 42
B. 48
C. 54
D. 60

Answer / उत्तर: B

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Q23

A batsman has an average of 50 runs after 20 innings. How many runs in the 21st innings are needed to increase average to 52?

A. 82
B. 90
C. 92
D. 100

Answer / उत्तर: C

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Q24

Average monthly income of a family for 4 months is ₹30,000 and for next 8 months ₹36,000. Annual monthly average is:

A. ₹32,000
B. ₹33,000
C. ₹34,000
D. ₹35,000

Answer / उत्तर: C

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Q25

Average temperature from Monday to Wednesday is 30°C and Tuesday to Thursday is 32°C. If Monday temperature is 28°C, Thursday temperature is:

A. 32°C
B. 34°C
C. 36°C
D. 38°C

Answer / उत्तर: B

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Q26

A man travels equal distances at 60 km/h and 40 km/h. Average speed is:

A. 48 km/h
B. 50 km/h
C. 52 km/h
D. 55 km/h

Answer / उत्तर: A

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Q27

A person travels equal distances at 30 km/h and 60 km/h. Average speed is:

A. 40 km/h
B. 45 km/h
C. 50 km/h
D. 55 km/h

Answer / उत्तर: A

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Q28

Average age of 5 persons is 24. A sixth person joins and average rises to 26. Sixth person's age is:

A. 32
B. 34
C. 36
D. 38

Answer / उत्तर: C

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Q29

Average of 10 numbers is 22. If each number is increased by 5, new average is:

A. 22
B. 25
C. 27
D. 32

Answer / उत्तर: C

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Q30

Average of 20 observations is 35. If every observation is multiplied by 3, new average becomes:

A. 70
B. 95
C. 105
D. 115

Answer / उत्तर: C