21. In a zoo, the entry fee for adults and children are Rs. 30 and Rs. 10 respectively. A 10 member family costs an average of Rs. 22. Find the total number of adults and children in the family.
एक चिड़ियाघर में, वयस्कों और बच्चों के लिए प्रवेश शुल्क क्रमशः 30 रुपये और 10 रुपये है। एक 10 सदस्यीय परिवार का खर्च औसतन रु. 22 है। परिवार में वयस्कों और बच्चों की कुल संख्या ज्ञात कीजिए।
Option “A” is correct.
Given:
The entry fee for adults = Rs. 30
The entry fee for children = Rs. 10
Average cost = Rs. 22
Concept used:
Total cost = (Average cost) × (Total number of persons)
Calculation:
Let the total number of adults be x
The total number of children be (10 – x)
⇒ Total cost = 22 × 10 = 220
Total cost = (The entry fee for adults) × (The total number of adults) + (The entry fee for children) × (The total number of children)
⇒ 220 = 30x + 10(10 – x)
⇒ 220 = 30x + 100 – 10x
⇒ 120 = 20x
⇒ x = 6
The total number of adults = x = 6
The total number of children = 10 – x = 10 – 6 = 4
∴ There are 6 adults and 4 children in the family.
22. The average of 12 numbers is 40. The average of the first seven numbers is 30 then finds the average of the remaining numbers? 12 संख्याओं का औसत 40 है। पहली सात संख्याओं का औसत 30 है तो शेष संख्याओं का औसत ज्ञात कीजिये?
Option “C” is correct.
Given:
The average of 12 numbers is 40 and the average of the first 7 numbers is 30.
Concept used:
Sum of all terms = Average × Total number of terms
Calculation:
The average of 12 numbers is 40
∴ Sum of numbers = 12 × 40 = 480
And, the average of the first 7 numbers is 30
∴ Sum of numbers = 7 × 30 = 210
Now, the sum of the remaining numbers = 480 – 210 = 270
∴ Average of remaining numbers = 270/5 = 54
23. Mean of 60 observations is 66. Later, it was found that an observation 24 was wrongly taken as 42. What is the corrected mean?
60 प्रेक्षणों का माध्य 66 है। बाद में यह पाया जाता है कि एक प्रेक्षण 24 को गलती से 42 लिया गया था। सही माध्य क्या है?
Option “A” is correct.
Given
Mean of 60 observations is 66 and
An observation 24 was wrongly taken as 42
Concept
Mean = (Sum of observation)/Total observation
Calculation
⇒ 66 = Sum of observation/ 60
⇒ Sum of observation = 60 × 66
⇒ Sum of observation = 3960
Now, From question
⇒ An observation 24 was wrongly taken as 42
⇒ Extra value = 42 – 24
⇒ Extra value = 18
So we need to subtract extra value from observation
⇒ New sum of observation = 3960 – 18
⇒ New sum of observation = 3942
⇒ New mean = 3942/60
⇒ New mean = 65.7
∴ New mean = 65.7
24. Find the average of all multiple of 5 from 243 to 572.
243 से 572 तक 5 के सभी गुणजों का औसत ज्ञात कीजिए।
Option “B” is correct.
Given:
To find the average of all multiple of 5 from 243 to 572
Concept:
Average will be equal to total sum divided by total number of terms
Formula used:
Sum = (n/2)(First term + Last term)
Average = Sum/n
Calculation:
Here,
First term = 245 (∵ should be divisible by 5)
Last term = 570
Sum = (n/2) × (245 + 570)
Average = Sum/n
⇒ [(n/2) × (245 + 570)]/n
⇒ (245 + 570)/2 = 407.5
∴ The average of all multiple of 5 from 243 to 572 = 407.5
25. A tenants consumed electricity first 10 days 10 unit/day next 10 days 20 unit/day and next 10 days 30 unit/day. What is the average unit consumed by tenants per day?
एक किरायेदार ने पहले 10 दिन 10 यूनिट / दिन अगले 10 दिन 20 यूनिट / दिन और अगले 10 दिन 30 यूनिट / दिन बिजली का उपभोग किया। प्रति दिन किरायेदार द्वारा उपभोग की जाने वाली औसत इकाई क्या है?
Option “B” is correct.
⇒ Consumed electricity in first 10 days = 10 × 10 = 100 unit
⇒ Consumed electricity in next 10 days = 20 × 10 = 200 unit
⇒ Consumed electricity in next 10 days = 30 × 10 = 300 unit
Total consumed electricity in one month = 100 + 200 + 300 = 600 unit
∴ Average required = 600/30 = 20 unit/day
26. The average of a series of 21 numbers is equal to 43. The average of the first eleven of them is 33. The average of the last eleven numbers is 53. The eleventh number of the series is:
21 संख्याओं की एक श्रृंखला का औसत 43 है। उनमें से पहली ग्यारह संख्याओं का औसत 33 है। अंतिम ग्यारह संख्याओं का औसत 53 है। श्रृंखला की ग्यारहवीं संख्या क्या है?
Option “D” is correct.
Average = sum of terms/number of terms
Sum of 21 numbers = 43 × 21 = 903
Sum of first 11 numbers = 33 × 11 = 363
Sum of last 11 numbers = 53 × 11 = 583
The eleventh number = 363 + 583 – 903 = 43
27.The average age of four brothers is 14 years. If their father is also included, the average is increased by 4 years. The age of the father (in years) is:
चार भाइयों की औसत आयु 14 वर्ष है। यदि उनके पिता को भी सम्मिलित कर लिया जाए, तब औसत4 वर्षों से बढ़ जाएगा। पिता की आयु (वर्षों में):
Option “C” is correct.
Average of four brothers = 14
Total age of four brothers = 14 × 4 = 56
After including father
New average = 14 + 4 = 18
Total age of four brothers and father = 18 × 5 = 90
∴ Age of father = 90 – 56 = 34
28. The average of 3 numbers is 7 and the average of first two numbers is 4. What is the third number?
3 संख्याओं का औसत 7 है और उनमें से पहली दो संख्याओं का औसत 4 है। तीसरी संख्या क्या है?
Option “B” is correct.
Given:
The average of 3 numbers = 7
The average of the first 2 numbers = 4
Formula used:
Average = (Sum of values/number of values)
Calculation:
The average of 3 numbers = 7
Sum of 3 numbers
⇒ 7 × 3
⇒ 21
The average of 2 numbers = 4
Sum of 2 numbers
⇒ 4 × 2
⇒ 8
Third Number = 21 – 8 = 13
∴ The third number is 13.
29. Two classes M and N have average marks 25 and 40 respectively. The overall average obtained is 30. The ratio of the students in the class M and N is:
दो कक्षा M और N का औसत अंक क्रमशः 25 और 40 हैं। प्राप्त कुल औसत 30 है। तो कक्षा M और N में छात्रों का अनुपात क्या है?
Option “A” is correct.
Let the number of students in two classes M and N are x and y respectively.
According to question,
The sum of marks obtained by all students in class M = 25x
And, the sum of marks obtained by all students in class N = 40y
⇒ The total marks obtained by all the students of both class = (25x + 40y)
⇒ The average marks obtained by all students of both class = (25x + 40y)/(x + y)
Again, according to question
(25x + 40y)/(x + y) = 30
⇒ 25x + 40y = 30x + 30y
⇒ 10y = 5x
⇒ x : y = 2 : 1
∴ The ratio of number of students of class M and class N are in the ratio 2 : 1
30. What is the average of first six natural numbers, which are multiples of 3?
पहली छह प्राकृतिक संख्याओं का औसत क्या है जो 3 के गुणज हैं?
Option “D” is correct.
The First 6 natural numbers which are multiples of 3 are 3, 6, 9, 12, 15, 18
⇒ Average = Sum of first 6 natural numbers multiple of 3/6
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