11. The average age of 24 students in a class is 15.5 years. The age of their teacher is 28 years more than the average of all twenty-five. What is the age of the teacher in years?
एक कक्षा में 24 छात्रों की औसत आयु 15.5. वर्ष है। उनके अध्यापक की आयु सभी 25 की औसत आयु से 28 वर्ष अधिक है। अध्यापक की आयु वर्ष में क्या है?
Option “C” is correct.
Given:
The average age of 24 students in a class is 15.5 years. The age of their teacher is 28 years more than the average of all twenty-five.
Formula Used:
average = sum of observation/number of observation
Calculation:
Average age of 24 students in the class = 15.5 years
⇒ Total age of 24 students = 24 × 15.5 = 372 years
Let age of teacher = x years and average age of all 25 = 372+x /25
⇒ x = 28 + 372+x25372+x/25
⇒ 25x – x = 700 + 372
⇒ x = 1072/24=134/3
Thus, age of teacher = 44 2/3years
12. The average age of students is A and the average age of teachers is B. The number of students is 45 times the number of teachers. What is the average age of students and teachers together?
छात्रों की औसत आयु A है और शिक्षकों की औसत आयु B है। छात्रों की संख्या शिक्षकों की संख्या से 45 गुना है। एक साथ छात्रों और शिक्षकों की औसत आयु क्या है?
Option “B” is correct.
Given:
The average age of students is A and the average age of teachers is B.
The number of students is 45 times the number of teachers.
Concept used:
Total = Mean × number of entities
Calculation:
The average age of students is A and the average age of teachers is B
Let total teachers be x
Number student = 45 × x
The average age of student = A
Total age of student = 45A × x
The average age of teachers = B
Total age of teachers = B × x
Average = (45Ax + Bx)/(x + 45x)
⇒ (45A + B)/46
∴ The average age of students and teachers together is (45A + B)/46.
13. The average age of husband, wife and their child 4 years ago was 26 years and that of wife and child 3 years ago was 22 years. What is the present age of the husband?
4 वर्ष पहले पति, पत्नी और उनके बच्चे की औसत आयु 26 वर्ष थी और 3 वर्ष पहले पत्नी और बच्चे की आयु 22 वर्ष थी। पति की वर्तमान आयु क्या है?
Option “D” is correct.
Given:
Average of ages 4 years ago = 26 years
Average of ages 3 years ago = 22 years
Formula used:
Average = (Sum of values)/(Number of values)
Calculation:
Let the present age of husband, wife and child be H, W and C respectively.
4 years ago,
{(H – 4) + (W – 4) + (C – 4)}/3 = 26
⇒ H + W + C – 12 = 78
⇒ H + W + C = 90
3 years ago,
{(W – 3) + (C – 3)}/2 = 22
⇒ W + C – 6 = 44
⇒ W + C = 50
Putting the value of W + C in equation (i),
H + W + C = 90
⇒ H + 50 = 90
⇒ H = 40
∴ The present age of the husband is 40 years.
14. The ratio of the present ages of A and B is 5 : 6. Eight years ago, the ratio of their ages was 4 : 5. What will be the ratio of the ages of A and B after 8 years from now?
A और B की वर्तमान आयु का अनुपात 5 : 6 है। आठ वर्ष पहले, उनकी आयु का अनुपात 4 : 5 था। अब से 8 वर्ष बाद A और B की आयु का अनुपात क्या होगा?
Given:
The ratio of the present ages of A and B is 5 : 6.
Eight years ago, the ratio of their ages was 4 : 5.
Calculation:
Let present ages of A and B be 5a and 6a respectively.
8 year ago age of A was (5a – 8) years
8 years ago age of B was (6a – 8) years
Accordingly,
(5a – 8) : (6a – 8) = 4 : 5
⇒ (5a – 8)/(6a – 8) = 4/5
⇒ 25a – 40 = 24a – 32
⇒ a = 8
Present age of A and B is 40 years and 48 years respectively
15. Five years ago, the average of the ages of 4 persons was 40 years. If a new person joins the group now, then the average of the ages of all five persons is 46 years. The age of the fifth person (in years) is:
पाँच वर्ष पहले, 4 व्यक्तियों की औसत आयु 40 वर्ष थी। यदि कोई नया व्यक्ति अब समूह में शामिल होता है, तो सभी पाँच व्यक्तियों की औसत आयु 46 वर्ष हो जाती है। पाँचवे व्यक्ति की आयु (वर्ष में) है:
Option “A” is correct.
Given:
5 years ago,
Average of 4 persons was 40 years.
Now,
Average of 5 persons is 46 years.
Formula Used:
Average = Sum of all observations/Total number of observations
Calclulation:
Five years ago,
The average of 4 persons was 40
⇒ 40 = Sum of ages of 4 persons/4
⇒ Sum of ages of 4 persons = 40 × 4
⇒ Sum of ages of 4 persons = 160 years
Present age = Age of a person 5 years ago + 5 year
⇒ The sum of current ages of all 4 members is,
⇒ 160 + 4 × 5
⇒ 160 + 20
⇒ 180 years.
Now 5th member is added and the average is 46 years.
⇒ 46 = Sum of ages of all 5 persons/5
⇒ Sum of ages of all 5 persons = 46 × 5
⇒ Sum of ages of all 5 persons = 230 years.
The age of 5th is,
⇒ 230 – 180
⇒ 50 years
∴ The age of the 5th person is 50 years.
16. In a group of 150 people, 2/5 are men, 1/3 are women and the rest are children. The average age of the women is 4/5 of the average age of the men. The average age of the children is 1/5 of the average age of the men. If the average age of the men is 50 years, then the average age of all the people in the group is?
150 लोगों के समूह में, 2/5 पुरुष हैं, 1/3 महिलाएं हैं और बाकी बच्चे हैं। महिलाओं की औसत आयु पुरुषों की औसत आयु का 4/5 है। बच्चों की औसत आयु पुरुषों की औसत आयु का 1/5 है। यदि पुरुषों की औसत आयु 50 वर्ष है, तो समूह में सभी लोगों की औसत आयु है?
Option “D” is correct.
Given:
Total people = 150
Average age of men = 50 years
Formula used:
Average = Sum of values/Number of values
Calculation:
Total men in the group = (2/5) × 150 = 60
Total women in the group = (1/3) × 150 = 50
Total children in the group = 150 – 60 – 50 = 40
Average age of men = 50 (given)
Average age of women = (4/5) × 50 = 40
Average age of children = (1/5) × 50 = 10
Now, Total age of men in the group = 60 × 50 = 3000
Total age of women in the group = 50 × 40 = 2000
Total age of children in the group = 40 × 10 = 400Total age of all persons in the group = 3000 + 2000 + 400 = 5400
Average age of persons in the group = 5400/150 = 36
∴ The average age of all the people in the group is 36
17.The sum of Vishal and Aditi’s current ages is 105 years. If Aditi is 25 years younger than Vishal, then what is the current age of Pritam who is 7 years older that Aditi?
विशाल और अदिति की वर्तमान आयु का योग 105 वर्ष है। अगर अदिति, विशाल से 25 साल छोटी है, तो प्रीतम की मौजूदा आयु क्या है जो अदिति से 7 साल बड़ा है?
Option “C” is correct.
According to the given information,
The sum of the current ages of Vishal and Aditi is 105 years.
Let the Vishal’s age be x
And the Aditi’s age be y
x + y = 105 —-(1)
If Aditi is 25 years younger than Vishal then,
x = y + 25 —-(2)
Putting value of equation (2) in equation (1),
y + 25 + y = 105
2y = 80
y = 40
y is Aditi’s present age, which is 40.
Pritam is 7 years older than Aditi
So Pritam’s age = y + 7 = 40 + 7 = 47.
Hence, the correct answer is47.
18. A mother said to her son, “When you were born, my age was equal to your present age”. If 5 years ago, son’s age was 16 years, then find the present age of mother..
एक मॉं ने अपने पुत्र से कहा, ”जब तुम पैदा हुए थे तो मेरी आयु तुम्हारी वर्तमान आयु के बराबर थी”। यदि 5 वर्ष पहले, पुत्र की आयु 16 वर्ष थी, तो मॉं की वर्तमान आयु ज्ञात कीजिये।
Option “A” is correct.
Given that :
Son’s age 5 years ago = 16 years.
Son’s present age = 16 + 5 = 21 years.
According to statement given,.
Mother’s age when son was born (21 years ago) = Present age of son.
Mother’s age 21 years ago = 21 years.
Mother’s present age = 21 + 21 = 42 years.
Hence, the correct answer is “42 years”.
19. The ratio of the present age of Mahesh and Ajay is 3 : 2 respectively. After 8 years. Ratio of their age will be 11: 8. What will be the present age of Mahesh’s son if his age is half of the present age of Ajay?
महेश और अजय की वर्तमान आयु का अनुपात क्रमशः 3 : 2 है। 8 वर्ष बाद, उनकी आयु का अनुपात 11 : 8 हो जाएगा। महेश के पुत्र की वर्तमान आयु क्या होगी, यदि उसकी आयु अजय की वर्तमान आयु की आधी है?
Option “C” is correct.
Given:
The ratio of the present age of Mahesh and Ajay is 3 : 2 respectively.
Ratio of their age will after 8 years 11: 8.
Calculation:
Let The present age of Mahesh be 3x years.
And The present age of Ajay be 2x years.
According to the question;
The ratio of their age will 8 years from now will be 11: 8,
⇒ (3x + 8)/(2x + 8) = 11/8
⇒ 8 × (3x + 8) = (2x + 8) × 11
⇒ 24x + 64 = 22x + 88
⇒ 24x – 22x = 88 –64
⇒ 2x = 24
⇒ x = 12
So, The present age of Ajay = 2x years = 2 × 12 = 24 years
∴ Mahesh’s Son age = 24/2 = 12 years.
20. The ratio between the present ages of A and B is 3 : 5. If the ratio of their ages five years after becomes 13 : 20, then the present age of B is:
A और B की वर्तमान आयु के बीच अनुपात 3 : 5 है। यदि पांच वर्ष बाद, उनकी आयु का अनुपात 13 : 20 हो जाता है, तो B की वर्तमान आयु है:
Option “B” is correct.
Given:
The ratio between the present ages of A and B is 3 : 5.
The ratio of their ages five years after becomes 13 : 20.
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