Age
problems involving percentages:
Question 1
There are three brothers x,y and z. If z's age is as much more than y's as y's age is more than x's age, find by how much percentage y is older than x. Hints: Age of z is 20 and y is 5 years older than x.
a. 100% b. 50% c. 25% d. 75%
Answer : b. 50%
Solution.:
Let a,b and c be the ages of x,y and z respectively.
It is given that z's age is as much more than y's as y's age is more than x's age.
Writing the above statement in the form of an equation, we get
c - b = b - a ...(1)
It is given that age of z i.e c = 20
Substituting c = 20 in eq 1 we get,
20 - b = b - a
20 = 2b - a ...(2)
It is also given that y is 5 years older than x. This implies b - a = 5 or b = a + 5...(3)
Substitute b = a + 5 in eq 2 we get,
20 = 2a + 10 - a
20 = a + 10 or a = 10
Substitute a = 10 in eq 3 we get
b = 15
Percentage by which b is more than a is (b - a)/a x 100% = (15 - 10)/10 x 100 = 50%
Question 2
John is 100% older than Johan. 20 years hence, John will be 50% older than Johan. Can you find their ages.
a. 30,20 b. 40,20 c. 60,40 d. 50,10
Answer : b. 40,20
Solution :
Let age of John be b.
Let age of Johan be a.
Currently John is 100% older than Johan. This implies b - a/a = 100%
Or (b - a)/a = 1 ( this is because, 100% = 100/100 = 1)
Or b - a = a
Or b = 2a ...(1)
20 years later ages of John and Johan will be b + 20 and a + 20 respectively
After 20 years John will be older by 50%
i.e (b + 20)-(a+20)/(a+20) = 50% = 1/2
(b - a)/ (a + 20) = 1/2
Or 2b - 2a = a + 20
Or 2b = 3a + 20 ...(2)
Substitute 1 in 2 we get
4a = 3a + 20 or a = 20.
Substitute a = 20 in eq 1 we get
b = 40
John's age is 40 and Johan's 20.
Question 3
Let a,b and c be ages of three brothers. b's age is greater than the sum of ages of a and c. After 7 years, by how much percentage b will be more than the sum of ages of a and c ?
a. (b - a - c - 7) / (a + c + 14) x 100% b. (b - a - c + 7) / (a + c + 14) x 100% c. (b - a - c) / (a + c + 7) x 100% d. (b - a - c - 7) / (a + c + 7) x 100%
Answer : a. (b - a - c - 7) / (a + c + 14) x 100%
Solution :
Percentage by which b's age will be greater than sum of a's and c's ages after 7 years
= Age of b after 7 years - (sum of ages of a and c after 7 years)
------------------------------------------------------------------------------------ x 100%
sum of ages of a and c after 7 years
= b + 7 - (a + 7 + c + 7)
--------------------------------- x 100%
a + 7 + c + 7
= (b - a - c - 7) / (a + c + 14) x 100%
Question 4
Four years ago, the average age of Deena and Prakash was 21 years. With Harish joining then now the average becomes 25 years. How old is Harish now?
a) 28 years b) 26 years c) 24 years d) 25 years.
Answer : d) 25 years.
Solution:
Let the present age of Deena, Prakash and Harish be A, B and C respectively.
4 years ago, the average age of Deena and Prakash was 21 years.
(i.e.) (A - 4 + B - 4) / 2 = 21
=> A + B = 50 -------- (1)
But now, the average age of Deena, Prakash and Harish is 25 years.
(i.e.) (A + B + C) / 3 = 25
=> A + B + C = 75 ------- (2)
(2) – (1) => C = 75 - 50 = 25.
Hence, the Present age of Harish is 25 years.
Question 5
The present age of Harini’s father is 4 times the present age of Harini. And the age difference of Harini’s father and mother is 5 years. Five years ago, the sum of all the three person’s age was 70 years. What is the present age of Harini’s father?
a)44years b) 40years c) 50years d) 48years
Answer : b) 40
Solution:
Let the Present ages of Father, Mother and Harini be F, M and H respectively.
Present age of Father = 4 * Present age of Harini
i.e. F = 4H ------- (1)
Age difference between Harini’s Parent's = 5
i.e. F – M = 5 -----------(2)
Five years ago, the sum of ages of Father, Mother and Harini is 70 years
i.e. F – 5 + M – 5 + H – 5 = 70
=> F + M + H = 85 -------- (3)
(2) + (3) => 2F + H = 90 ----- (4)
Substitute (1) in (4), we get H = 10.
Then F = 4*10 = 40.
Therefore the present age of Harini’s father is 40 years.
Question 6
Haritha told her friends that if she add ten times her age ten years from now to five times her age five years ago is same as the 20 times of her current age. How old Haritha will be ten years from now?
a)15 years b) 20 years c) 23 years d) 25 years
Answer : d) 25 years
Solution:
Let the age of Haritha be X.
Then, 10 times her age after 10 years + 5 times her age before 5 years = 20 times her present age.
i.e. 10 * (X + 10) + 5 * (X - 5) = 20 * X
15X + 75 = 20X
5X = 75
X = 15
Hence, Haritha’s Present age is 15 years.
So, after 10 years, Haritha’s age will be 25 years.
Question 7
Three years ago, the ages of Geetha, Reena and Surya are in the ratio of 3:4:5. Three years hence, the sum of their ages is 78. What is the age of Reena at present?
a)18 years b) 23 years c) 28 years d) 20 years
Answer : b) 23 years
Solution:
Let the ages of Geetha, Reena and Surya 3 years ago be 3X, 4X and 5X respectively.
After 3 years, the sum of their ages is 78.
i.e. (3X + 3) + 3 + (4X + 3) + 3 + (5X + 3) + 3 = 78
12X = 60
X = 5.
Hence, Reena’s present age is 4X + 3 = 4(5) + 3 = 23 years
Question 8
Ramesh Khanna was five times old as his son Kishan Khanna eight years ago. Now he is three times as old as his son Kishan Khanna. Assume they both live in a country where people understand only binary numbers and they use symbol '0' for binary 1 and '1' for binary zero. Also they add 1 before any binary number. Express Ramesh Khanna’s present age in accordance to that world
a) 1001111 b) 1001111 c) 1100011 d) 1010000
Answer : a) 1001111
Solution :
Let Ramesh Khanna’s age be represented as ‘F’ eight years ago and the age of Kishan Khanna be represented as ‘S”.
F = 5 S
F + 8 = 3 (S + 8)
5S + 8 = 3S + 24
5S – 3 S = 24 – 8
2S = 16
S = 8
Now Ramesh Khanna’s age will be 5S + 8 = (5x8) + 8 = 48
Expressed as binary 110000 . However the people in their country use symbol 0 for binary one and 1 for binary zero. Replacing 1 with 0 and 0 with 1 we get 001111. Also those people usually add 1 before any binary number. Hence the answer becomes 1001111.
Question 9
Bhavna is presently three times as old as her daughter Anushka. Ten years ago Bhavna was five times as old as her daughter Anushka was. After how many years, sum of their ages will be 100.
a) 10 b) 20 c)15 d) none of these.
Answer : a) 10
Solution :
Let Bhavna’s present age be represented as B
Let her daughter Anushka’s age be represented as A.
B = 3 A
Ten years ago,
B - 10 = 5(A – 10)
3A - 10 = 5A - 50
-10 + 50 = 5A – 3A = 2 A
40 = 2 A
A = 20.
B = 3 x A = 60.
Present sum of their ages = A + B = 80.
When 10 is added to both A and B, Sum of their ages will become 100. Hence, after 10 years, their sum of ages will be 100.
Question 10
Monisha was seven times as old as her daughter Mercy eight years ago. Now three times Mercy’s age is her mother age. Before how many years the ratio of their ages (ratio of mother's age to Mercy's age) will be increased by 1 from the current ratio
a) 5 b) 4 c) 8 d) none of these.
Answer : b) 4
Solution :
Eight years ago -- let Monisha’s age be M and Mercy’s age be D.
M = 7 D
Now M + 8 = 3 (D + 8)
7 D + 8 = 3D + 24
7D - 3 D = 24 - 8 = 16
D = 4 = age of Mercy before 8 years
M = 28 = age of Mother before 8 years
Current age of Mercy = D + 8 = 12
Current age of Monisha = M + 8 = 36
Current ratio of mother's age to Mercy's age = 36/12 = 3.
Let before x years this ratio becomes 1 more than the current ratio. i.e x denotes the number of years before which the ratio becomes 3 + 1 = 4.
Then 36 - x / 12 - x = 4
36 - x = 48 - 4x
3x = 12
Or x = 4
i.e before 4 years, the ratio of their ages will be 4. Therefore answer = 4
Question 1
There are three brothers x,y and z. If z's age is as much more than y's as y's age is more than x's age, find by how much percentage y is older than x. Hints: Age of z is 20 and y is 5 years older than x.
a. 100% b. 50% c. 25% d. 75%
Answer : b. 50%
Solution.:
Let a,b and c be the ages of x,y and z respectively.
It is given that z's age is as much more than y's as y's age is more than x's age.
Writing the above statement in the form of an equation, we get
c - b = b - a ...(1)
It is given that age of z i.e c = 20
Substituting c = 20 in eq 1 we get,
20 - b = b - a
20 = 2b - a ...(2)
It is also given that y is 5 years older than x. This implies b - a = 5 or b = a + 5...(3)
Substitute b = a + 5 in eq 2 we get,
20 = 2a + 10 - a
20 = a + 10 or a = 10
Substitute a = 10 in eq 3 we get
b = 15
Percentage by which b is more than a is (b - a)/a x 100% = (15 - 10)/10 x 100 = 50%
Question 2
John is 100% older than Johan. 20 years hence, John will be 50% older than Johan. Can you find their ages.
a. 30,20 b. 40,20 c. 60,40 d. 50,10
Answer : b. 40,20
Solution :
Let age of John be b.
Let age of Johan be a.
Currently John is 100% older than Johan. This implies b - a/a = 100%
Or (b - a)/a = 1 ( this is because, 100% = 100/100 = 1)
Or b - a = a
Or b = 2a ...(1)
20 years later ages of John and Johan will be b + 20 and a + 20 respectively
After 20 years John will be older by 50%
i.e (b + 20)-(a+20)/(a+20) = 50% = 1/2
(b - a)/ (a + 20) = 1/2
Or 2b - 2a = a + 20
Or 2b = 3a + 20 ...(2)
Substitute 1 in 2 we get
4a = 3a + 20 or a = 20.
Substitute a = 20 in eq 1 we get
b = 40
John's age is 40 and Johan's 20.
Question 3
Let a,b and c be ages of three brothers. b's age is greater than the sum of ages of a and c. After 7 years, by how much percentage b will be more than the sum of ages of a and c ?
a. (b - a - c - 7) / (a + c + 14) x 100% b. (b - a - c + 7) / (a + c + 14) x 100% c. (b - a - c) / (a + c + 7) x 100% d. (b - a - c - 7) / (a + c + 7) x 100%
Answer : a. (b - a - c - 7) / (a + c + 14) x 100%
Solution :
Percentage by which b's age will be greater than sum of a's and c's ages after 7 years
= Age of b after 7 years - (sum of ages of a and c after 7 years)
------------------------------------------------------------------------------------ x 100%
sum of ages of a and c after 7 years
= b + 7 - (a + 7 + c + 7)
--------------------------------- x 100%
a + 7 + c + 7
= (b - a - c - 7) / (a + c + 14) x 100%
Question 4
Four years ago, the average age of Deena and Prakash was 21 years. With Harish joining then now the average becomes 25 years. How old is Harish now?
a) 28 years b) 26 years c) 24 years d) 25 years.
Answer : d) 25 years.
Solution:
Let the present age of Deena, Prakash and Harish be A, B and C respectively.
4 years ago, the average age of Deena and Prakash was 21 years.
(i.e.) (A - 4 + B - 4) / 2 = 21
=> A + B = 50 -------- (1)
But now, the average age of Deena, Prakash and Harish is 25 years.
(i.e.) (A + B + C) / 3 = 25
=> A + B + C = 75 ------- (2)
(2) – (1) => C = 75 - 50 = 25.
Hence, the Present age of Harish is 25 years.
Question 5
The present age of Harini’s father is 4 times the present age of Harini. And the age difference of Harini’s father and mother is 5 years. Five years ago, the sum of all the three person’s age was 70 years. What is the present age of Harini’s father?
a)44years b) 40years c) 50years d) 48years
Answer : b) 40
Solution:
Let the Present ages of Father, Mother and Harini be F, M and H respectively.
Present age of Father = 4 * Present age of Harini
i.e. F = 4H ------- (1)
Age difference between Harini’s Parent's = 5
i.e. F – M = 5 -----------(2)
Five years ago, the sum of ages of Father, Mother and Harini is 70 years
i.e. F – 5 + M – 5 + H – 5 = 70
=> F + M + H = 85 -------- (3)
(2) + (3) => 2F + H = 90 ----- (4)
Substitute (1) in (4), we get H = 10.
Then F = 4*10 = 40.
Therefore the present age of Harini’s father is 40 years.
Question 6
Haritha told her friends that if she add ten times her age ten years from now to five times her age five years ago is same as the 20 times of her current age. How old Haritha will be ten years from now?
a)15 years b) 20 years c) 23 years d) 25 years
Answer : d) 25 years
Solution:
Let the age of Haritha be X.
Then, 10 times her age after 10 years + 5 times her age before 5 years = 20 times her present age.
i.e. 10 * (X + 10) + 5 * (X - 5) = 20 * X
15X + 75 = 20X
5X = 75
X = 15
Hence, Haritha’s Present age is 15 years.
So, after 10 years, Haritha’s age will be 25 years.
Question 7
Three years ago, the ages of Geetha, Reena and Surya are in the ratio of 3:4:5. Three years hence, the sum of their ages is 78. What is the age of Reena at present?
a)18 years b) 23 years c) 28 years d) 20 years
Answer : b) 23 years
Solution:
Let the ages of Geetha, Reena and Surya 3 years ago be 3X, 4X and 5X respectively.
After 3 years, the sum of their ages is 78.
i.e. (3X + 3) + 3 + (4X + 3) + 3 + (5X + 3) + 3 = 78
12X = 60
X = 5.
Hence, Reena’s present age is 4X + 3 = 4(5) + 3 = 23 years
Question 8
Ramesh Khanna was five times old as his son Kishan Khanna eight years ago. Now he is three times as old as his son Kishan Khanna. Assume they both live in a country where people understand only binary numbers and they use symbol '0' for binary 1 and '1' for binary zero. Also they add 1 before any binary number. Express Ramesh Khanna’s present age in accordance to that world
a) 1001111 b) 1001111 c) 1100011 d) 1010000
Answer : a) 1001111
Solution :
Let Ramesh Khanna’s age be represented as ‘F’ eight years ago and the age of Kishan Khanna be represented as ‘S”.
F = 5 S
F + 8 = 3 (S + 8)
5S + 8 = 3S + 24
5S – 3 S = 24 – 8
2S = 16
S = 8
Now Ramesh Khanna’s age will be 5S + 8 = (5x8) + 8 = 48
Expressed as binary 110000 . However the people in their country use symbol 0 for binary one and 1 for binary zero. Replacing 1 with 0 and 0 with 1 we get 001111. Also those people usually add 1 before any binary number. Hence the answer becomes 1001111.
Question 9
Bhavna is presently three times as old as her daughter Anushka. Ten years ago Bhavna was five times as old as her daughter Anushka was. After how many years, sum of their ages will be 100.
a) 10 b) 20 c)15 d) none of these.
Answer : a) 10
Solution :
Let Bhavna’s present age be represented as B
Let her daughter Anushka’s age be represented as A.
B = 3 A
Ten years ago,
B - 10 = 5(A – 10)
3A - 10 = 5A - 50
-10 + 50 = 5A – 3A = 2 A
40 = 2 A
A = 20.
B = 3 x A = 60.
Present sum of their ages = A + B = 80.
When 10 is added to both A and B, Sum of their ages will become 100. Hence, after 10 years, their sum of ages will be 100.
Question 10
Monisha was seven times as old as her daughter Mercy eight years ago. Now three times Mercy’s age is her mother age. Before how many years the ratio of their ages (ratio of mother's age to Mercy's age) will be increased by 1 from the current ratio
a) 5 b) 4 c) 8 d) none of these.
Answer : b) 4
Solution :
Eight years ago -- let Monisha’s age be M and Mercy’s age be D.
M = 7 D
Now M + 8 = 3 (D + 8)
7 D + 8 = 3D + 24
7D - 3 D = 24 - 8 = 16
D = 4 = age of Mercy before 8 years
M = 28 = age of Mother before 8 years
Current age of Mercy = D + 8 = 12
Current age of Monisha = M + 8 = 36
Current ratio of mother's age to Mercy's age = 36/12 = 3.
Let before x years this ratio becomes 1 more than the current ratio. i.e x denotes the number of years before which the ratio becomes 3 + 1 = 4.
Then 36 - x / 12 - x = 4
36 - x = 48 - 4x
3x = 12
Or x = 4
i.e before 4 years, the ratio of their ages will be 4. Therefore answer = 4
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