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Question 1 of 5
1. Question
Eight years ago, the ages of the members of a joint family of ten people added up to 300 years. Two years later, one member died at the age of 65 years and a child was born during the same year. After another two years, one more member died, again at 65, and a child was born during the same year. The current average age of the ten-member joint family is (in years):
Correct
Answer: Option (b)
Explanation:
Total age of all the ten people in the family eight years ago was = 300 years
As per the information given in the question, there will be increase of 2 years in age of each of the members. So increase in total age = 2 x 10
Age of infant will be taken as 0
Therefore, the total age of all the people in the family six years ago = 300 + 2×10 – 65 + 0 = 255 years
Similarly, the total age of all the people in the family four years ago = 255 +2×10 – 65 + 0 = 210 years
Since time difference is 4 years, therefore there will be an increase of 4 years in age of each member of the family.
So, Total age = 210 + 4 x 10 = 250 years
Therefore, the current average age of all the people in the family = 250/10
= 25 years.
Incorrect
Answer: Option (b)
Explanation:
Total age of all the ten people in the family eight years ago was = 300 years
As per the information given in the question, there will be increase of 2 years in age of each of the members. So increase in total age = 2 x 10
Age of infant will be taken as 0
Therefore, the total age of all the people in the family six years ago = 300 + 2×10 – 65 + 0 = 255 years
Similarly, the total age of all the people in the family four years ago = 255 +2×10 – 65 + 0 = 210 years
Since time difference is 4 years, therefore there will be an increase of 4 years in age of each member of the family.
So, Total age = 210 + 4 x 10 = 250 years
Therefore, the current average age of all the people in the family = 250/10
= 25 years.
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Question 2 of 5
2. Question
The average age of 60 students is 20 years. When 15 new students are admitted, the average increases by 0.4 years. What must be the average age of the new students?
Correct
Answer: Option (a)
Explanation:
Let the average age of the newly admitted 15 students be x years.
So, Total age of 15 newly admitted students = 15x
Since given average age of existing 60 students = 20
Therefore, Total age of the existing 60 students = 60×20
Hence, total age of the 75 students = 60×20 + 15x
Since average after admission of new students increases by 0.4 years. So new average = 20.4 years
So, 60×20 + 15x =75×20.4
Or 1200 + 15x = 1530
Or 15x = 1530-1200
Or 15x = 330
Or x = 330/15
Or x = 22 years
Incorrect
Answer: Option (a)
Explanation:
Let the average age of the newly admitted 15 students be x years.
So, Total age of 15 newly admitted students = 15x
Since given average age of existing 60 students = 20
Therefore, Total age of the existing 60 students = 60×20
Hence, total age of the 75 students = 60×20 + 15x
Since average after admission of new students increases by 0.4 years. So new average = 20.4 years
So, 60×20 + 15x =75×20.4
Or 1200 + 15x = 1530
Or 15x = 1530-1200
Or 15x = 330
Or x = 330/15
Or x = 22 years
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Question 3 of 5
3. Question
In a neighbourhood, 12% of the people are less than 30 years of age, 6% of the people are more than 70 years old, 22% of the people are more than 50 years old and 990 people are between 30 years and 50 years of age. How many people are between 50 and 70 years of age?
Correct
Answer: Option (b)
Explanation:
Percentage of people less than 30 years of age = 12%; Percentage of people more than 70 years of age = 6%;
Percentage of people more than 50 years of age = 22%
Number of people between 30 and 50 years of age= 990.
Percentage of people between 30 and 50 years = 100% – 12% – 22% = 66%
Let the total number of people be X
So, 66% of X = 990
Thus, X = (990/66) × 100 = 1,500
People between 50 and 70 years = 22 – 6 = 16% of 1500 = 240
Hence, option (b) is the correct answer.
Incorrect
Answer: Option (b)
Explanation:
Percentage of people less than 30 years of age = 12%; Percentage of people more than 70 years of age = 6%;
Percentage of people more than 50 years of age = 22%
Number of people between 30 and 50 years of age= 990.
Percentage of people between 30 and 50 years = 100% – 12% – 22% = 66%
Let the total number of people be X
So, 66% of X = 990
Thus, X = (990/66) × 100 = 1,500
People between 50 and 70 years = 22 – 6 = 16% of 1500 = 240
Hence, option (b) is the correct answer.
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Question 4 of 5
4. Question
A man’s age was a perfect cube when his son was born. A couple of years later, he had a daughter. What is the possible sum of the ages of man, his son and his daughter when the man’s age becomes a perfect cube again?
Correct
Answer: Option (a)
Explanation:
The man’s age can be 27 when the son was born.
Daughter was born when he was 29.
His age will be a perfect cube again when he is 64.
Sum of ages of man, his son and his daughter = 64 + (64 -29) + (64 -27) = 136 years.
Note: The other perfect cubes, 8 and 64 are not appropriate as per the given options.
Incorrect
Answer: Option (a)
Explanation:
The man’s age can be 27 when the son was born.
Daughter was born when he was 29.
His age will be a perfect cube again when he is 64.
Sum of ages of man, his son and his daughter = 64 + (64 -29) + (64 -27) = 136 years.
Note: The other perfect cubes, 8 and 64 are not appropriate as per the given options.
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Question 5 of 5
5. Question
There are two types of employees, executives and managers in a company. If the average age of the executives is 34 years and the average age of all the eomployees is 38 years. if total number of employees is 25 and total number of managers is 10, then what is the average age (in year) of managers?
Correct
Answer: Option (c)
Explanation:
Number of managers = 10
Number of executives = 15
So, the ratio of number of executives to number of managers = 3:2
Now by using alligation
(38 – 34) / (X – 38) = 2/3
4/(X – 38) = 2/3
6 = X – 38
X = 44 years
Incorrect
Answer: Option (c)
Explanation:
Number of managers = 10
Number of executives = 15
So, the ratio of number of executives to number of managers = 3:2
Now by using alligation
(38 – 34) / (X – 38) = 2/3
4/(X – 38) = 2/3
6 = X – 38
X = 44 years
