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Average and Age Questions
61. Shivam is 4 years younger than Mayank while Divyanshi is 4 years younger than Samrat but one-fifth times as old as Shivam. If Samrat is eight years old, how many times as old is Mayank as Divyanshi?
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Correct Ans:6 times
Explanation:
Given, the present age of Samrat = 8 years
Then, the present age of Divyanshi = present age of Samrat - 4 = 8 - 4 = 4 years
Given, Divyanshi is one-fifth times as old as Shivam
---> present age of Divyanshi = (1/5) * present age of Shivam
---> present age of Shivam = 5 * present age of Divyanshi = 5 * 4 = 20 years
Given, Shivam is 4 years younger than Mayank
Then, Mayank is 4 years older than Shivam.
---> present age of Mayank = present age of Shivam + 4 = 20 + 4 = 24 years
Now, present age of Divyanshi * 6 times = 4 * 6 = 24 which is Mayank's present age.
Thus, Mayank is 6 times older than Divyanshi.
Then, the present age of Divyanshi = present age of Samrat - 4 = 8 - 4 = 4 years
Given, Divyanshi is one-fifth times as old as Shivam
---> present age of Divyanshi = (1/5) * present age of Shivam
---> present age of Shivam = 5 * present age of Divyanshi = 5 * 4 = 20 years
Given, Shivam is 4 years younger than Mayank
Then, Mayank is 4 years older than Shivam.
---> present age of Mayank = present age of Shivam + 4 = 20 + 4 = 24 years
Now, present age of Divyanshi * 6 times = 4 * 6 = 24 which is Mayank's present age.
Thus, Mayank is 6 times older than Divyanshi.
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62. A professional institute's total expenditure on students for a particular course is partly fixed and partly varies linearly with the number of students. The average expense per student is Rs. 615 when there are 24 students and Rs. 465 when there are 40 students. What is the average expense when there are 60 students?
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Correct Ans:Rs. 390
Explanation:
Let partially fixed expenditure be x and partially varying expenditure be y.
Given, when there are 24 students, average expense per student = Rs. 615
---> Total expense = Rs. 615 * number of students
---> Now, Total expense = partially fixed expenditure + expenditure partially varying with the number of students
Then, Total expense = 615 * 24 = x + 24 y
---> x + 24y = 14760 ---> eqn (1)
Similarly, when there are 40 students,
Total expense = 465 * 40 = x + 40 y
----> x + 40y = 18600 ---> eqn (2)
Now, eqn (2) - eqn (1) [ie., subtraction], we get,
40y - 24y = 18600 - 14760
---> 16y = 3840
---> y = 240
Then, From eqn (1), x = 14760 - 24 * 240
---> x = 14760 - 5760
---> x = 9000
When there are 60 students, Total expense = x + 60 y
= 9000 + 60 * 240
= 23400
Average expense when there are 60 students = 23400/60
= 390
Given, when there are 24 students, average expense per student = Rs. 615
---> Total expense = Rs. 615 * number of students
---> Now, Total expense = partially fixed expenditure + expenditure partially varying with the number of students
Then, Total expense = 615 * 24 = x + 24 y
---> x + 24y = 14760 ---> eqn (1)
Similarly, when there are 40 students,
Total expense = 465 * 40 = x + 40 y
----> x + 40y = 18600 ---> eqn (2)
Now, eqn (2) - eqn (1) [ie., subtraction], we get,
40y - 24y = 18600 - 14760
---> 16y = 3840
---> y = 240
Then, From eqn (1), x = 14760 - 24 * 240
---> x = 14760 - 5760
---> x = 9000
When there are 60 students, Total expense = x + 60 y
= 9000 + 60 * 240
= 23400
Average expense when there are 60 students = 23400/60
= 390
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63. A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
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Correct Ans:18 years
Explanation:
Let the present age of the person = x
Then, his age three years hence = x + 3
multiply it by 3 ---> (x + 3) * 3
Then subtract three times his age three years ago ---> [(x + 3) * 3] - [3 * (x - 3)]
Now, present age of the person = x = [(x + 3) * 3] - [3 * (x - 3)]
---> x = [3x + 9] - [3x -9]
---> x = 3x + 9 - 3x + 9
---> x = 18
Thus, the present age of the person = x = 18 years
Then, his age three years hence = x + 3
multiply it by 3 ---> (x + 3) * 3
Then subtract three times his age three years ago ---> [(x + 3) * 3] - [3 * (x - 3)]
Now, present age of the person = x = [(x + 3) * 3] - [3 * (x - 3)]
---> x = [3x + 9] - [3x -9]
---> x = 3x + 9 - 3x + 9
---> x = 18
Thus, the present age of the person = x = 18 years
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64. The average salary of the whole employees in a company is Rs. 300 per day. The average salary of officers is Rs. 800 per day and that of clerks is Rs. 240 per day. If the number of officers is 30, then find the number of clerks in the company?
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Correct Ans:250
Explanation:
Let the number of clerks in the company be x.
Given, average salary of officers = Rs. 800 per day
Number of officers = 30
---> Total salary of officers = Average salary * Number of officers
= 800 * 30
= Rs. 24,000
Given, average salary of clerks = Rs. 240 per day
Then, Total salary of clerks = 240 * x
= 240x
Given, average salary of whole employees = Rs. 300 per day
---> Total salary of whole employees = Average salary * [Number of officers + Number of clerks]
= 300 * [30 + x]
Now, Total salary of whole employees = Total salary of officers + Total salary of clerks
---> 300 * [30 + x] = 24000 + 240x
---> 9000 + 300x = 24000 + 240x
---> 300x - 240x = 24000 - 9000
---> 60x = 15000
---> x = 250
Thus, the number of clerks in the company = x = 250 members.
Given, average salary of officers = Rs. 800 per day
Number of officers = 30
---> Total salary of officers = Average salary * Number of officers
= 800 * 30
= Rs. 24,000
Given, average salary of clerks = Rs. 240 per day
Then, Total salary of clerks = 240 * x
= 240x
Given, average salary of whole employees = Rs. 300 per day
---> Total salary of whole employees = Average salary * [Number of officers + Number of clerks]
= 300 * [30 + x]
Now, Total salary of whole employees = Total salary of officers + Total salary of clerks
---> 300 * [30 + x] = 24000 + 240x
---> 9000 + 300x = 24000 + 240x
---> 300x - 240x = 24000 - 9000
---> 60x = 15000
---> x = 250
Thus, the number of clerks in the company = x = 250 members.
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65. The average age of Rinku and Ridipta is 18 years. When Rita replaces Ridipta, the average age is increased by 1 and when Ridipta replaces Rinku the average age becomes 17 years. What is the age of Rita?
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Correct Ans:18 years
Explanation:
Given, average age of Rinku and Ridipta = 18 years
---> Total age of Rinku and Ridipta = Average * 2
= 18 * 2 = 36
---> Rinku + Ridipta = 36 ---> eqn(1)
When Rita replaces Ridipta,
Average age of Rinku and Rita = 19 years
---> Total age of Rinku and Rita = 19 * 2 = 38
---> Rinku + Rita = 38 ---> eqn(2)
When Ridipta replaces Rinku,
Average age of Ridipta and Rita = 17 years
---> Total age of Ridipta and Rita = 17 * 2 = 34
---> Ridipta + Rita = 34 ---> eqn(3)
Now, Subtracting eqns (1) and (2) i.e., eqn (2) - eqn (1), we get,
Rita - Ridipta = 38 - 36
---> Rita - Ridipta = 2 ---> eqn (4)
Now, eqn(3) + eqn (4), we get
2 Rita = 34 + 2
--> Rita = 36/2
---> Rita = 18
Thus, the age of Rita = 18 years.
---> Total age of Rinku and Ridipta = Average * 2
= 18 * 2 = 36
---> Rinku + Ridipta = 36 ---> eqn(1)
When Rita replaces Ridipta,
Average age of Rinku and Rita = 19 years
---> Total age of Rinku and Rita = 19 * 2 = 38
---> Rinku + Rita = 38 ---> eqn(2)
When Ridipta replaces Rinku,
Average age of Ridipta and Rita = 17 years
---> Total age of Ridipta and Rita = 17 * 2 = 34
---> Ridipta + Rita = 34 ---> eqn(3)
Now, Subtracting eqns (1) and (2) i.e., eqn (2) - eqn (1), we get,
Rita - Ridipta = 38 - 36
---> Rita - Ridipta = 2 ---> eqn (4)
Now, eqn(3) + eqn (4), we get
2 Rita = 34 + 2
--> Rita = 36/2
---> Rita = 18
Thus, the age of Rita = 18 years.
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66. In the afternoon, a student read 100 pages at the rate of 60 pages per hour. In the evening, when she was tired, she read next 100 pages at the rate of 40 pages per hour. What was her average rate of reading, in pages per hour?
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Correct Ans:48
Explanation:
Number of hours the student read in the afternoon = Number of pages/ rate
= 100 / 60
= 5/3
Number of hours the student read in the evening = Number of pages/ rate
= 100 / 40
= 5/2
Total hours of reading = (5/3) + (5/2)
= (10 + 15) / 6
= 25/6
Total pages read = 100 + 100 = 200
Average rate of reading = Total pages read / Total hours of reading
= 200 / (25/6)
= (200 * 6)/25
= 8 * 6
= 48 pages per hour
= 100 / 60
= 5/3
Number of hours the student read in the evening = Number of pages/ rate
= 100 / 40
= 5/2
Total hours of reading = (5/3) + (5/2)
= (10 + 15) / 6
= 25/6
Total pages read = 100 + 100 = 200
Average rate of reading = Total pages read / Total hours of reading
= 200 / (25/6)
= (200 * 6)/25
= 8 * 6
= 48 pages per hour
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67. The sum of the present ages of Arun and Nithin is 9 times the difference of the age of Arun and Nithin. Arun is elder than Nithin. 6 years hence, their total ages will be 12 times the difference of their ages. What is the present age of Arun who is elder than Nithin?
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Correct Ans:20 years
Explanation:
Let the present ages of Arun and Nithin be A and N.
Given, A + N = 9 (A - N)
---> A + N = 9A - 9N
---> N + 9 N = 9A - A
---> 10N = 8A
---> 5N = 4A
----> A/N = 5/4
---> The ratio of present ages of Arun and Nithin, A : N = 5 : 4
---> present age of Arun ie., A = 5x
present age of Nithin ie., N = 4x
6 years hence,
(A + 6) + (N + 6) = 12 [(A + 6) - (N + 6)]
---> (5x + 6) + (4x + 6) = 12 [5x + 6 - 4x - 6]
---> 9x + 12 = 12 [x]
---> 12x - 9x = 12
---> 3x = 12
---> x = 4
Hence, present age of Arun ie., A = 5x = 5 * 4 = 20 years
Given, A + N = 9 (A - N)
---> A + N = 9A - 9N
---> N + 9 N = 9A - A
---> 10N = 8A
---> 5N = 4A
----> A/N = 5/4
---> The ratio of present ages of Arun and Nithin, A : N = 5 : 4
---> present age of Arun ie., A = 5x
present age of Nithin ie., N = 4x
6 years hence,
(A + 6) + (N + 6) = 12 [(A + 6) - (N + 6)]
---> (5x + 6) + (4x + 6) = 12 [5x + 6 - 4x - 6]
---> 9x + 12 = 12 [x]
---> 12x - 9x = 12
---> 3x = 12
---> x = 4
Hence, present age of Arun ie., A = 5x = 5 * 4 = 20 years
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68. The average weight of a group of boys and girls is 38 kg. The average weight of boys is 42 kg and that of girls is 33 kg. If the number of boys is 25, then find the number of girls.
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Correct Ans:20
Explanation:
Let number of girls = x
Given, Average weight of boys = 42 kg
Number of boys = 25
Then, Total weight of boys = Average weight of boys * Number of boys
= 42 * 25
= 1050
Given, Average weight of girls = 33 kg
Then, Total weight of girls = 33 * x = 33x
Now, Total weight of boys and girls = 1050 + 33x ---> eqn (1)
Given, Average weight of a group of boys and girls = 38 kg
---> Total weight of boys and girls = Average weight of a group of boys and girls * (No. of boys + No. of girls)
---> Total weight of boys and girls = 38 (25 + x) ---> eqn (2)
From eqn (1) and (2),
1050 + 33x = 38 (25 + x)
---> 1050 + 33x = 950 + 38x
---> 38x - 33x = 1050 - 950
---> 5x = 100
---> x = 100/5
---> x = 20
Thus, number of girls = x = 20
Given, Average weight of boys = 42 kg
Number of boys = 25
Then, Total weight of boys = Average weight of boys * Number of boys
= 42 * 25
= 1050
Given, Average weight of girls = 33 kg
Then, Total weight of girls = 33 * x = 33x
Now, Total weight of boys and girls = 1050 + 33x ---> eqn (1)
Given, Average weight of a group of boys and girls = 38 kg
---> Total weight of boys and girls = Average weight of a group of boys and girls * (No. of boys + No. of girls)
---> Total weight of boys and girls = 38 (25 + x) ---> eqn (2)
From eqn (1) and (2),
1050 + 33x = 38 (25 + x)
---> 1050 + 33x = 950 + 38x
---> 38x - 33x = 1050 - 950
---> 5x = 100
---> x = 100/5
---> x = 20
Thus, number of girls = x = 20
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69. A's age is one-sixths of B's age. B's age will be twice of C's age after 10 years. If C's eighth birthday was celebrated two years ago, then the present age of A must be:
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Correct Ans:5 years
Explanation:
Let A be the age of person 'A'
B be the age of person 'B'
and C be the age of person 'C'
Given, A = (1/6)B ---> eqn (1)
B + 10 = 2 (C + 10) ---> eqn (2)
If C's eighth birthday was celebrated two years ago, then present age of C must be 10 years.
Substitute C = 10 in eqn (2), we get
B + 10 = 2 (10 + 10)
---> B = 2 (20) - 10
---> B = 40 - 10
---> B = 30
Thus, present age of B = 30 years.
Now From eqn (1)
A = (1/6) * 30
---> A = 5
Hence, present age of A = 5 years.
B be the age of person 'B'
and C be the age of person 'C'
Given, A = (1/6)B ---> eqn (1)
B + 10 = 2 (C + 10) ---> eqn (2)
If C's eighth birthday was celebrated two years ago, then present age of C must be 10 years.
Substitute C = 10 in eqn (2), we get
B + 10 = 2 (10 + 10)
---> B = 2 (20) - 10
---> B = 40 - 10
---> B = 30
Thus, present age of B = 30 years.
Now From eqn (1)
A = (1/6) * 30
---> A = 5
Hence, present age of A = 5 years.
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70. The average monthly income of 4 earning members of a family is Rs. 7,350. One member passes away and the average monthly income becomes Rs. 6,500. What was the monthly income of the person, who is no more?
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Correct Ans:Rs. 9,900
Explanation:
Given, average monthly income of 4 family members = Rs. 7350
---> Total Monthly income of 4 members = 7350 * 4 = 29,400
Average monthly income of 3 persons (excluding the dead person) = Rs. 6500
----> Total Monthly income of remaining 3 persons = 6500 * 3 = 19,500
Therefore, Monthly income of dead person = 29,400 - 19,500 = Rs. 9,900
---> Total Monthly income of 4 members = 7350 * 4 = 29,400
Average monthly income of 3 persons (excluding the dead person) = Rs. 6500
----> Total Monthly income of remaining 3 persons = 6500 * 3 = 19,500
Therefore, Monthly income of dead person = 29,400 - 19,500 = Rs. 9,900
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71. The average age of a class of 39 students is 15 yr. If the age of the teacher is included, then the average increases by 3 months. Find the age of the teacher.
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Correct Ans:25
Explanation:
Average age of 39 students = 15 yr
Age of 39 students = 39 * 15 = 585 yr
Average age of students and teacher = 15 + 3 months = 15 + 3/12 = 61/4 yr
Age of students and teacher = 40 * 61/4 = 610 yr
Hence, age of teacher = 610 - 585 = 25 yr
Age of 39 students = 39 * 15 = 585 yr
Average age of students and teacher = 15 + 3 months = 15 + 3/12 = 61/4 yr
Age of students and teacher = 40 * 61/4 = 610 yr
Hence, age of teacher = 610 - 585 = 25 yr
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72. The average age of group of 20 girls is 15 yr and that of another group of 25 boys is 24 yr. The average age of the two groups mixed together is
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Correct Ans:20 yr
Explanation:
Given, average age of 20 girls = 15 yr
Average age of 25 boys = 24 yr
Age of 20 girls = 15 * 20 = 300 yr
Similarly, age of 25 boys = 24 * 25 = 600 yr
Now, the average age of the two groups = (Age of girls + Age of boys)/(Total number of boys and girls)
= (300 + 600)/(20 + 25)
= 900/45 = 20 yr
Average age of 25 boys = 24 yr
Age of 20 girls = 15 * 20 = 300 yr
Similarly, age of 25 boys = 24 * 25 = 600 yr
Now, the average age of the two groups = (Age of girls + Age of boys)/(Total number of boys and girls)
= (300 + 600)/(20 + 25)
= 900/45 = 20 yr
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73. The average age of a husband and his wife was 23 years at the beginning of their marriage. After five years they have a one-year old child. The average age of the family of three, when the child was born, was
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Correct Ans:18 years
Explanation:
Husband age + wife age (at the time of marriage)= 23 * 2 = 46
After 5 years of marriage = Husband + wife + child
= 46 + 10 + 1 = 57 years
At the time of birth of child = 57 - 3
= 54 years
Required average age = 54/3 = 18 years
After 5 years of marriage = Husband + wife + child
= 46 + 10 + 1 = 57 years
At the time of birth of child = 57 - 3
= 54 years
Required average age = 54/3 = 18 years
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74. The average age of four boys A, B, C and D is 5 years and the average age of A, B, D, E is 6 years. C is 8 years old. The age of E is (in years)
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Correct Ans:12
Explanation:
Given, the average age of A, B, C and D = 5 years
---> (A + B + C + D) / 4 = 5
---> A + B + C + D = 5 * 4
---> A + B + C + D = 20 years ----> eqn (i)
Also, given that, average age of A, B, D, E = 6 years
---> (A + B + D + E) / 4 = 6
---> A + B + D + E = 6 * 4
---> A + B + D + E = 24 years ----> eqn (ii)
On Solving eqn (i) - eqn (ii) [ie., subtracting], we get
C - E = - 4
Given that, age of C = 8 years
---> 8 - E = -4
---> E = 8 + 4 = 12 years
Hence, the age of E = 12 years.
---> (A + B + C + D) / 4 = 5
---> A + B + C + D = 5 * 4
---> A + B + C + D = 20 years ----> eqn (i)
Also, given that, average age of A, B, D, E = 6 years
---> (A + B + D + E) / 4 = 6
---> A + B + D + E = 6 * 4
---> A + B + D + E = 24 years ----> eqn (ii)
On Solving eqn (i) - eqn (ii) [ie., subtracting], we get
C - E = - 4
Given that, age of C = 8 years
---> 8 - E = -4
---> E = 8 + 4 = 12 years
Hence, the age of E = 12 years.
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75. The mean of 11 numbers is 35. If the mean of first 6 numbers is 32 and that of the last six numbers is 37, find the sixth number.
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Correct Ans:29
Explanation:
Given Mean of 11 numbers = 35
Formula:- Mean (or) Average = Sum of numbers/Total no. of elements
So, sum of 11 numbers = 35 * 11 = 385
Similarly, sum of first 6 numbers = 32 * 6 = 192
and sum of last six numbers = 37 * 6 = 222
Now, the sixth number = (192 + 222) - 385
= 414 - 385
= 29
Formula:- Mean (or) Average = Sum of numbers/Total no. of elements
So, sum of 11 numbers = 35 * 11 = 385
Similarly, sum of first 6 numbers = 32 * 6 = 192
and sum of last six numbers = 37 * 6 = 222
Now, the sixth number = (192 + 222) - 385
= 414 - 385
= 29
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76. The average of 8 numbers is 14. The average of 6 of these numbers is 16. What is the average of the remaining two numbers?
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Correct Ans:8
Explanation:
Average of 8 numbers = 14
Sum of 8 numbers = 14*8 = 112
Similarly, average of 6 numbers = 16
Sum of 6 numbers = 16*6 = 96
Therefore,
Sum of remaining two numbers = Sum of 8 numbers - Sum of 6 numbers
= 112 - 96 = 16
Average = Sum of two number/2
=16/2
Average =8
Sum of 8 numbers = 14*8 = 112
Similarly, average of 6 numbers = 16
Sum of 6 numbers = 16*6 = 96
Therefore,
Sum of remaining two numbers = Sum of 8 numbers - Sum of 6 numbers
= 112 - 96 = 16
Average = Sum of two number/2
=16/2
Average =8
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77. The sum of present age of Rahul and Abishek is 48 years. Today Abishek is 4 years older than Shweta. The respective ratio of the present ages of Rahul and Shweta is 4 : 7 What was Abishek"™s age two years ago?
SHOW ANSWER
Correct Ans:30 years
Explanation:
Let present ages of Rahul and Swetha be 4X and 7X respectively
Present age of Abishek = 7X + 4
sum of the present ages of Rahul and Abishek is 48 years
=> 4X + (7X + 4) = 48
=> 11X = 44
=> X = 4
Present age of Abishek = 7X + 4 = 7*4 + 4 = 32
Abishek's age two years ago = 32 - 2 = 30
Present age of Abishek = 7X + 4
sum of the present ages of Rahul and Abishek is 48 years
=> 4X + (7X + 4) = 48
=> 11X = 44
=> X = 4
Present age of Abishek = 7X + 4 = 7*4 + 4 = 32
Abishek's age two years ago = 32 - 2 = 30
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78. An HR Company employs 4800 persons, out of which 45 percent are males and 60 percent of the males are either 25 years or older. How many males are employed in that HR Company who are younger than 25 years?
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Correct Ans:864
Explanation:
Total employees = 4800
45% of employees are males = 45/100 * 4800
= 2160
60% of 2160 are equal to or older than 25
So, 40% of 2160 are younger than 25 years = 40/100 * 2160
= 864
45% of employees are males = 45/100 * 4800
= 2160
60% of 2160 are equal to or older than 25
So, 40% of 2160 are younger than 25 years = 40/100 * 2160
= 864
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79. Nine persons went to a hotel for taking their meals. Eight of them spent Rs.12 each over their meals and their ninth spent Rs. 8 more than the average expending of all the nine. Total money spent by them was:
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Correct Ans:Rs.117
Explanation:
No. of persons = 9
Let the average expenditure of 9 persons be x
Now according to question,
12 * 8 + (x+8) / 9 = x
96 + x + 8 = 9x
8x = 104
x = 13
Total money spent by 9 persons = 9x
9*13 =Rs.117
Let the average expenditure of 9 persons be x
Now according to question,
12 * 8 + (x+8) / 9 = x
96 + x + 8 = 9x
8x = 104
x = 13
Total money spent by 9 persons = 9x
9*13 =Rs.117
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80. Average of present age of P and R is 33 years. Q is 18 years older than R and Q is 6 years younger than S. If present age of P is 33(1/3)% less than present age of S, then find average of present age of Q, R and S.
SHOW ANSWER
Correct Ans:44 years
Explanation:
Let the present ages of P, Q, R and S be P, Q, R, and S respectively.
Given that, (P + R) / 2 = 33
---> P + R = 66 ---> eqn (i)
Q = R + 18 ---> eqn (ii)
Q = S - 6 ---> eqn (iii)
P = S - 33(1/3)% of S
---> P = S - (100/3)% of S
---> P = S - [(100/3)/100] * S
---> P = S - (1/3) * S
---> P = (3S - S) / 3
---> P = 2S/3 ---> eqn (iv)
Put the value of eqn (iv) in eqn (i), we get
(2S/3) + R = 66 ---> eqn (v)
Put the value of Q from eqn (ii) in eqn (iii), we get
R + 18 = S - 6
---> S - R = 18 + 6
---> S - R = 24 ---> eqn (vi)
On Adding eqn (v) and eqn (vi)
(2S/3) + S = 66 + 24
---> (2S + 3S)/3 = 90
---> 5S = 270
---> S = 54 which is the present age of S.
Now, from eqn (iii), the present age of Q = S - 6 = 48
Now, from eqn (ii), the present age of R = Q - 18 = 30
Thus, Required average = (48 + 30 + 54)/3
= 132/3
= 44 years
Given that, (P + R) / 2 = 33
---> P + R = 66 ---> eqn (i)
Q = R + 18 ---> eqn (ii)
Q = S - 6 ---> eqn (iii)
P = S - 33(1/3)% of S
---> P = S - (100/3)% of S
---> P = S - [(100/3)/100] * S
---> P = S - (1/3) * S
---> P = (3S - S) / 3
---> P = 2S/3 ---> eqn (iv)
Put the value of eqn (iv) in eqn (i), we get
(2S/3) + R = 66 ---> eqn (v)
Put the value of Q from eqn (ii) in eqn (iii), we get
R + 18 = S - 6
---> S - R = 18 + 6
---> S - R = 24 ---> eqn (vi)
On Adding eqn (v) and eqn (vi)
(2S/3) + S = 66 + 24
---> (2S + 3S)/3 = 90
---> 5S = 270
---> S = 54 which is the present age of S.
Now, from eqn (iii), the present age of Q = S - 6 = 48
Now, from eqn (ii), the present age of R = Q - 18 = 30
Thus, Required average = (48 + 30 + 54)/3
= 132/3
= 44 years
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