Average Questions for Competitive Exams

11. The average of five consecutive even numbers is M. If the next five even numbers are also included, the average of ten numbers will be:

पांच क्रमागत सम संख्याओं का औसत M है। यदि अगले पांच सम संख्याओं को भी शामिल कर दिया जाता है, तो दस संख्याओं का औसत क्या होगा?

M + 10
10
11
M + 5

Option “D” is correct.

Let the five consecutive even numbers are 2, 4, 6, 8, 10.

Average of consecutive even numbers = (2 + 4 + 6 + 8 + 10)/5 = 30/5 = 6

Hint: As we know, Average of any AP is the median so, the average = 6

So, M = 6

If the next five even numbers are also included, then the numbers are

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Average of 10 consecutive numbers = (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)/10 = 110/10 = 11

Hint: As we know, Average is the median so, the average = 11

We can write 11 = 6 + 5 or M + 5

12. 24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:

24 छात्रों ने दान के लिए पैसे जमा किये। औसत योगदान 50 रुपए था। बाद में उसके शिक्षक ने भी कुछ पैसों का योगदान दिया। अब औसत योगदान 56 रुपए है। तो शिक्षक का योगदान क्या है?

Rs. 56
Rs. 200
Rs. 106
Rs. 194

Option “B” is correct.

Average contribution of 24 students = 50

Sum of contribution of 24 students = 50 × 24 = 1200

Average contribution of 25 persons (24 students and 1 teacher) = 56

Sum of contribution of 25 persons = 56 × 25 = 1400

∴ Contribution of teacher = 1400 – 1200 = 200

13. A student’s mark was wrongly entered as 108 instead of 98. Due to this mistake, the average marks of the class got increased by 1/5. Total number of students in the class is equal to

किसी छात्र के अंक को गलत तरीके से 98 के बजाय 108 के रूप में दर्ज किया गया था। इस गलती के कारण कक्षा का औसत अंक 1/5 बढ़ गया। कक्षा में कुल छात्रों की संख्या बराबर है।

Option “C” is correct.

Let, number of students in class = x

Average marks of the class = y

According to the question,

⇒ x(y + 1/5) = xy + 108 – 98

⇒ xy + x/5 = xy + 10

⇒ x/5 = 10

⇒ x = 50

∴ Number of students in the class = 50

14. The average of 10 two-digit positive integers is A. by mistake, one number xy is taken as yx, then the average increases by 6.3. What is the value of the difference of digits (Difference between x and y)?

10 दो अंकीय धनात्मक पूर्णांकों का औसत ए है गलती से, एक संख्या xy को yx के रूप में लिया गया है, तो औसत 6.3 से बढ़ जाता है। अंकों के अंतर का मान क्या है (x और y के बीच अंतर)?

Option “A” is correct.

The average of integers is A

Then, we know that

Average = $\frac{s u m o f a l l t h e n u m b e r s}{T o t a l n o o f t e r m s}$

⇒ A = $\frac{s u m o f a l l t h e n u m b e r s}{10}$

⇒ Sum of numbers = 10A

According to the question

⇒ A + 6.3 = $\frac{s u m o f a l l t h e n u m b e r s - (10 x + y) + (x + 10 y)}{10}$

⇒ A + 6.3 = $\frac{10 A - (10 x + y) + (x + 10 y)}{10}$

⇒ 10A + 63 = 10A – 9x + 9y

⇒ y – x = 7

So, the difference of digits is 7

Hence, option (A) is correct

15. 30 pens and 75 pencils were purchased for Rs. 390. If the average price of a pencil is Rs. 2.00, then calculate the average price (in Rs.) of a pen.

30 पेन और 75 पेंसिल 390 रु. में खरीदे गए थे। यदि एक पेंसिल का औसत मूल्य 2.00 रु. है, तो एक पेन के औसत मूल्य (रु. में) की गणना कीजिए।

A. 6

B. 4

C. 8

D. 12

Option “A” is correct.

Let, average price of a pen = Rs x

According to the question,

⇒ 30x + 75 × 2 = 390

⇒ 30x = 390 – 150

⇒ 30x = 240

⇒ x = 8

∴ Average price of a pen = Rs. 8

16. Average weight of students and teachers in a school is 48 kg. If the average weight of all students is 45 kg and that of all teachers is 72 kg then what is the ratio of the total numbers of students and the teachers in the school?

किसी विद्यालय में छात्रों और शिक्षकों का औसत वजन 48 किलोग्राम है। यदि सभी छात्रों का औसत वजन 45 किलोग्राम और सभी शिक्षकों का औसत वजन 72 किलोग्राम है तब विद्यालय में छात्रों और शिक्षकों की कुल संख्या का अनुपात क्या है?

25 : 1
18 : 1
8 : 1
16 : 1

Option “C” is correct.

Let’s consider numbers of students and teachers is x and y respectively.

According to the questions, we get

(x + y) × 48 = 45x + 72y

Or, x(48 – 45) = y(72 – 48)

Or, 3x = 24y

Or, x/y = 24/3

Or, x : y = 8 : 1

17.The average weight of 30 students in a class is 25 kgs. If the weight of the class teacher is added, the average weight increase by 2 kgs. The weight of the class teacher (in kgs) is:

एक कक्षा में 30 छात्रों का औसत वजन 25 किग्रा है। यदि शिक्षक का वजन शामिल किया जाता है, तो औसत वजन में 2 किग्रा की वृद्धि होती है। शिक्षक का वजन (किग्रा में) क्या है?

A. 86

B. 84

C. 81

D. 87

Option “C” is correct.

Given:

Average weight of 30 students = 25 kg

Calculation:

Sum of weight of 30 students = 30 × 25 = 750

Let the weight of teacher be x

New average weight of 31 (30 students and 1 teacher) = 27

⇒ (750 + x)/31 = 27

⇒ 750 + x = 837

⇒ x = 837 – 750 = 87

∴ Weight of teacher = 837 – 750 = 87

18. A cricketer has an average of 56 after playing 22 innings. How many runs should he score in the next inning so as the new average is 54?

एक क्रिकेटर का 22 पारियों को खेलने के बाद औसत 56 है। अगली पारी में उसे कितने रन बनाने चाहिए ताकि नया औसत 54 हो जाए?

Option “B” is correct.

Average of 22 innings = 56

⇒ Sum of runs after 22 innings = 56 × 22 = 1232

Now, average of 23 innings = 54

⇒ Sum of runs after 23 innings = 23 × 54 = 1242

∴ Score in 23^rd innings = 1242 – 1232 = 10 runs

19. Find the value of the middle number if the average of 5 numbers in a group is 30. Given that the average of the first two numbers is 30.5 and that of the last two numbers is 34.

मध्य संख्या का मान ज्ञात कीजिए यदि एक समूह में 5 संख्याओं का औसत 30 है। दिया गया है कि पहली दो संख्याओं का औसत 30.5 है और अंतिम दो संख्याओं का औसत 34 है।

Option “B” is correct.

Given:

Average of 5 numbers in a group is 30

Average of the first two numbers is 30.5

Average of the last two numbers is 34

Concept used:

Average × Numbers + Average × Numbers = overall Average × Total Numbers

Calculation:

Let the value of the middle number be ‘x’

30.5 × 2 + x + 34 × 2 = 30 × 5

⇒ 61 + x + 68 = 150

⇒ x = 21

∴ Middle number = 21

20. There are four employees in the company and their weights are 40 kg, 60 kg, 50 kg and 30 kg respectively. Find their average weight.

एक कंपनी में चार कर्मचारी हैं और उनका वज़न क्रमशः 40 किग्रा, 60 किग्रा, 50 किग्रा और 30 किग्रा है। उनका औसत वज़न ज्ञात कीजिये।

40 kg
45 kg
50 kg
60 kg

Option “B” is correct.

Given:

Four person’s weight = 40 kg, 60 kg, 50 kg, 30 kg

Concept:

Average = Total sum/ Total persons

Calculation:

Sum of weights = 40 + 60 + 50 + 30

= 180

Average weight = Total weight / Number of persons

= 180/4

= 45 kg

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2 thoughts on “Average Questions for Competitive Exams”

Arvind kumar
14 January 2025 at 07:27

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