Age
Concept
Age related problems are basically brain teaser. This types of math is provided to find out the absolute age of a person or another. Here some secondary data is provided in passive way exposing hints comparing another person to find out actual age of that person applying basic mathematical rules or equation.
Tips to solve age related problems:
- If the present age of a person is x, then the age before n years will be (x-n) years.
- If the present age of a person is x, then the age after n years will be (x+n) years.
- If the present age of a person is x, then n times the current age will be (x×n) years.
- If the age is given in the form of a ratio, such as, p:q, then the age shall be considered as qx and px, where x is common factor.
Q. A father is 30 years older than his son. In 10 years, the father will be three times as old as the son. How old are they now?
A) 15 and 45
B) 5 and 35
Answer:
Let x be the son's age. Father's age=X+30.
After 10 years, father and son's age respectively X+40 and X+10.
According to question,
X+40=3(X+10)
Or, X+40=3x+30
Or, 2x=10
Or, x=5
Hence, ages of father =30+5=35 and son=5 years.
Let x be the son's age. Father's age=X+30.
After 10 years, father and son's age respectively X+40 and X+10.
According to question,
X+40=3(X+10)
Or, X+40=3x+30
Or, 2x=10
Or, x=5
Hence, ages of father =30+5=35 and son=5 years.
C) 12 and 42
D) 8 and 38
Discuss
Q. A mother is four times as old as her daughter. In six years, the mother will be twice as old as the daughter. How old are they now?
A) 12 and 48
B) 9 and 36
C) 6 and 24
D) 3 and 12
Answer:
Let x be the daughter's age. Mother's age=4x.
After 6 years, mother and daughter's age respectively 4x+6 and X+6.
According to question,
4x+6=2(X+6)
Or, 4x+6=2x+12
Or, 2x=6
Or, x=3
Hence, age of mother =4x=4x33=12.
Let x be the daughter's age. Mother's age=4x.
After 6 years, mother and daughter's age respectively 4x+6 and X+6.
According to question,
4x+6=2(X+6)
Or, 4x+6=2x+12
Or, 2x=6
Or, x=3
Hence, age of mother =4x=4x33=12.
Discuss
Q. A grandfather is six times as old as his grandson. The sum of their ages is 63. How old are they now?
A) 9 and 54
Answer:
Let x be the grandson’s age, and grandfather=6x
their ratio of ages=x:6x=1:6.
Now, Grandfather's age=63x(6/7)=54 and Grandson's age=63x(1/7)=9.
Let x be the grandson’s age, and grandfather=6x
their ratio of ages=x:6x=1:6.
Now, Grandfather's age=63x(6/7)=54 and Grandson's age=63x(1/7)=9.
B) 10 and 60
C) 7 and 42
D) 6 and 36
Discuss
Q. A teacher is thrice as old as one of his students. Four years later, the teacher would be 10 more than twice the age of the student. How old are they now?
A) 16 and 48
B) 12 and 36
C) 14 and 42
Let, present age of the teacher=3x & student=x.
According to question,
3x+4=2(x+4)+10
Or, 3x+4=2x+18
Or, x=14
According to question,
3x+4=2(x+4)+10
Or, 3x+4=2x+18
Or, x=14
D) 18 and 36
Discuss
Q. A brother is five years older than his sister. The product of their ages is 150. How old are they now?
A) 8 and 13
B) 10 and 15
Let, age of sister=x, brother=x+5.
According to question,
x(x+5)=150
Or, x^2+5x-150=0
Or, X^2+15x-10x-150=0
Or, x(x+15)-10(x+15)=0
Or, x=10.
They are now 10 and 15 years.
According to question,
x(x+5)=150
Or, x^2+5x-150=0
Or, X^2+15x-10x-150=0
Or, x(x+15)-10(x+15)=0
Or, x=10.
They are now 10 and 15 years.
C) 12 and 17
D) 14 and 19
Discuss
Q. A father is three times as old as his son. Six years ago, the father was four times as old as the son. How old are they now?
A) 15 and 45
B) 18 and 54
Let, age of son=x, father=3x
According to question,
3x-6=4(x-6)
Or, 3x-6=4x-24
Or, x=18
Hence, Age of son=18 and father=3x18=54.
According to question,
3x-6=4(x-6)
Or, 3x-6=4x-24
Or, x=18
Hence, Age of son=18 and father=3x18=54.
C) 20 and 60
D) 24 and 72
Discuss
Q. A mother is fifteen years older than her son. The difference between their ages is three-fifth of the mother’s age. How old the son will be in 5 years?
A) 45
B) 33
C) 25
Let, age of son=x, Mother=x+15.
According to question,
(x+15)-x=[(x+15)x3]/5
Or, 75=3x+45
Or, 3x=30
Or, x=10
According to question,
(x+15)-x=[(x+15)x3]/5
Or, 75=3x+45
Or, 3x=30
Or, x=10
D) 37
Discuss
Q. A grandmother is eight times as old as her granddaughter. The difference between their ages is equal to the granddaughter’s age. How old are they now?
A) Both are zero years old.
B) Both are negative eight years old.
C) None of these
Description is not available. Let’s discuss.
D) Both are eight years old.
Discuss
Q. A father is seven times older than his son. The sum of their ages is equal to the square of the son’s age. How old are they now?
A) 45 and 12
B) 40 and 9
C) 56 and 8
Let, age of son=x, father=7x.
According to question,
7x+x=x^2
Or, 8x=XxX
Or, x=8.
Thus, age of son=8 and father=7x8=56.
According to question,
7x+x=x^2
Or, 8x=XxX
Or, x=8.
Thus, age of son=8 and father=7x8=56.
D) None of these
Discuss
Q. The average age of girls in the class is one-third the number of boys in the class. The ratio of boys and girls in the class is 3:1. What is the sum of the ages of girls in the class if the number of students in the class is 32?
A) 54
B) 73
C) 64
Answer:
No. of boys=(32/4)x3=24
No. of girls=32-24=8
Average age of girls=24x(1/3)=8
Sum of the ages of girls=Average Age x No. of Girls
Sum of Ages of Girls=8x8=64.
No. of boys=(32/4)x3=24
No. of girls=32-24=8
Average age of girls=24x(1/3)=8
Sum of the ages of girls=Average Age x No. of Girls
Sum of Ages of Girls=8x8=64.
D) 78
Discuss
Q. Three years ago the average age of A and B was 22.50. After joining C the average age of them after three years will be 30. How old is C now?
A) 36
B) 43
C) 46
D) 30
Answer:
Three years ago total age of A and B =22.50x2=45
Now, total age of A and B = 45+(3x2)=51
After three years total age of A, B & C=30x3=90
Now, total age of the three=90-9=81
So, present age of C = 81-51=30.
Three years ago total age of A and B =22.50x2=45
Now, total age of A and B = 45+(3x2)=51
After three years total age of A, B & C=30x3=90
Now, total age of the three=90-9=81
So, present age of C = 81-51=30.
Discuss
Q. One year ago a father was four times as old as his son. In 8 years, his age exceeds twice his son’s age by 11 years. What is the present age of father?
A) 41
Answer:
Let, 1 year ago the age of son=X. Father’s age=4X.
In 8 years, son and father’s age respectively=X+9 and 4X+9.
According to question,
4x+9=2(x+9)+11
Or, 4x+9=2x+18+11
Or, 4x+9=2x+29
Or, 2x=20
Or,x=10
Now father’s age=4x+1=4x10+1=41
Let, 1 year ago the age of son=X. Father’s age=4X.
In 8 years, son and father’s age respectively=X+9 and 4X+9.
According to question,
4x+9=2(x+9)+11
Or, 4x+9=2x+18+11
Or, 4x+9=2x+29
Or, 2x=20
Or,x=10
Now father’s age=4x+1=4x10+1=41
B) 40
C) 49
D) 53
Discuss
Q. Ratio of father's age to son's age is 9:1. The product of their ages is 81. What will be the ratio of their ages after three years?
A) 9:1
B) 5:1
Answer:
Let, x be the common factor for both of them.
So, father's age will be 9x and son's age will be x.
Product of their ages=9x^2=81, or, x^2=9, or, x=3.
After three years ratio will be=(27+3):(3+3)=30:6=5:1
Let, x be the common factor for both of them.
So, father's age will be 9x and son's age will be x.
Product of their ages=9x^2=81, or, x^2=9, or, x=3.
After three years ratio will be=(27+3):(3+3)=30:6=5:1
C) 7:2
D) 4:3
Discuss
Q. After six years the ratio of ages of father and son will be 14:5; whereas, six years ago, he was ten times as old as his son was. What is the father's present age?
A) 43
B) 36
Answer:
let, x be the common factor.
After 6 years, ages of father and son will be 14x and 5x.
Accordingly,
(14x-12)=10(5x-12)
or, 14x-12=50x-120
or, 36x=108
or, x=3.
So, father's age now is (14×3)-6=36.
let, x be the common factor.
After 6 years, ages of father and son will be 14x and 5x.
Accordingly,
(14x-12)=10(5x-12)
or, 14x-12=50x-120
or, 36x=108
or, x=3.
So, father's age now is (14×3)-6=36.
C) 48
D) 39
Discuss
Q. In ten years, A will be three times as old as ten years ago. If a is now 20 years older than B, what will be the age of A after 3 years?
A) 76
B) 42
C) 63
D) 53
Answer:
Let, present age of B = X years.
Present age of A=x+20 years.
Accordingly,
(x+20)+10= 3(x-10)
or, x+30=3x-30
or, 2x=60
x=30.
After 3 years the age of A will be 30+20+3=53.
Let, present age of B = X years.
Present age of A=x+20 years.
Accordingly,
(x+20)+10= 3(x-10)
or, x+30=3x-30
or, 2x=60
x=30.
After 3 years the age of A will be 30+20+3=53.
Discuss
