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# Aptitude::Problems on Ages

Home > Quantitative Aptitude > Problems on Ages > Subjective Solved Examples

Example 1 / 22

What is Jack's present age, if after 22 years his age will be 4 times his age 5 years back?
Let Jack's present age be x
Jack's age before 5 years = (x - 5)
Jack's age after 22 years = (x + 22)
We are given that, Jack's age after 22 years (x + 22) is 4 times his age 5 years back (x – 5)
Therefore,
(x + 22) = 4(x – 5)
Solving the equation, we get
x + 22 = 4x – 20
3x = 42
x = 14 years Ans.

If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A: B, then A: B will be Ay and By
NA
NA

Example 2 / 22

Rahul is 16 years elder than Rohan. If 4 years ago, Rahul was 5 times as old as Rohan, then find Rahul's present age.
Let age of Rohan be y
Rahul is 16 years elder than Rohan = (y + 16).
So Rahul's age 4 years ago = (y + 16 – 4)
Rohan's age before 4 years = (y – 4)
4 years ago, Rahul is 5 times as old as Rohan
Thus, we can have the equation as,
(y + 16 – 4) = 5 (y – 4)
(y + 12) = (5y – 20)
4y = 32
y = 8
Rohan's age = 8 years
Rahul's age = (y + 16) = (8+16) = 24 years Ans.

If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 3 / 22

One year ago, the ratio of Paul and Peter age's was 5:6 respectively. After 4 years, this ratio becomes 6:7. How old is Peter?
We are given that age ratio of Paul: Peter = 5:6
Let,
Paul's age = 5x and Peter's age = 6x
1 year ago, their age was 5x and 6x.
Hence at present,
Paul's age = 5x +1
Peter's age = 6x +1
Now after 4 years,
Paul's age = (5x +1) + 4 = (5x + 5)
Peter's age = (6x +1) + 4 = (6x + 5)
Hence,
After 4 years, this ratio becomes 6 : 7. Therefore,

$$\frac{Paul's age}{6}$$= $$\frac{Peter's age}{7}$$
$$\frac{(5x+5}{6x+5}$$= $$\frac{6}{7}$$
7 (5x + 5) = 6 (6x + 5)
X = 5
Peter's present age = (6x + 1) = (6 x 5 + 1) = 31 years
Paul's present age = (5x + 1) = (5 x 5 + 1) = 26 years Ans.

If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 4 / 22

If the sum of ages of x and y is A and ratio of their ages is p : q respectively, then u can determine the age of y by using the formula shown below:
Age of y= $$\frac{ratio of y}{sum of ratios}$$* sum of ages
Age of y= $$\frac{q}{p+q}$$* A Ans.

If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 5 / 22

Age of mother 10 years ago was 6 times the age of her son. After 10 years, mother's age will be twice that of his son. Find the ratio of their present ages.
Let 10 years ago, age of son be x and so mother's age= 6x.
At present,
Mother's age will be (6x + 10) and son's age will be (x + 10)
After 10 years,
Mother's age will be (6x + 10) +10 and son's age will be (x + 10) + 10
Mother's age is twice that of son
(6x + 10) +10 = 2 [(x + 10) + 10]
(6x + 20) = 2[x + 20]
Solving the equation, we get x = 5
Therefore, the present ratio.
(6x + 10) : (x + 10) = 70 : 15 = 14:3 Ans.

If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 6 / 22

Raj is 40 years old and Surya is 60 years old. How many years ago was the ratio of their ages 4 : 8?
Let us assume x years ago.
At present,
Raj's age= 40 years
Surya's age= 60 years
x years ago;
Raj's age = (40 – x)
Surya's age = (60 – x)
Also,
Ratio of their ages x years ago was 4 : 8

$$\frac{(40-x)}{(60-x)}$$= $$\frac{4}{8}$$
8(40 – x) = 4(60 – x)
320 – 6x = 240 – 4x
x = 40
Therefore, 40 years ago, the ratio of their ages was 4 : 8.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 7 / 22

The ratio of Rohan's age 4 years ago and Rahul's age after 4 years is 1 : 1. If at present, the ratio of their ages is 5 : 3, then find the ratio between Rohan's age 4 years hence and Rahul's age 4 years ago.
At present;
Ratio of their ages = 5 : 3.
Therefore, let it be 5x and 3x.
Rohan's age 4 years ago = 5x – 4
Rahul's age after 4 years = 3x + 4
Now;
Ratio of Rohan's age 4 years ago and Rahul's age after 4 years is 1 : 1
Therefore,
Solving, we get;;
$$\frac{(5x-4)}{(3x+4)}$$= $$\frac{1}{1}$$
So, x=4.
Now;
the ratio between Rohan's age 4 years hence and Rahul's age 4 years ago will be=
Rohan's age : (5x + 4)
Rahul's age: (3x – 4)
So, Rahul's age: Rohan's age
$$\frac{(5x+4)}{(3x-4)}$$
= $$\frac{24}{8}$$
= $$\frac{3}{1}$$= 3:1
If sum of ages of x and y is A and ratio of their ages is p : q respectively, then u can determine age of y by using the formula shown below:

Age of y= $$\frac{ratio of y}{sum of ratios}$$* sum of ages
Age of y= $$\frac{q}{p+q}$$* A
NA
NA

Example 8 / 22

5 years ago, sister's age was 5 times the age of her brother and the sum of the present ages of sister and brother is 34 years. What will be the age of her brother after 6 years?
We are given, 5 years ago sister's age was 5 times the age of her brother.
Therefore,
(34 – x) – 5 = 5 (x – 5)
34 – x – 5 = 5x – 25
5x + x = 34 – 5 +25
6x = 54
x = 9
So, after 6 yrs
(x + 6)
= (9 + 6) = 15 years
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 9 / 22

Father is 2 times more aged than his daughter. If after 6 years, he would be 2 times of daughter's age, then further after 6 years, how many times he would be of his daughter's age?
Let daughter's age be x and father's age be 2x.
Father's age is 3 times more aged than his daughter, therefore father's present age = x + 2x = 3x
After 5 years, father's age is 3 times more than his daughter age.
(3x + 6) = 2(x + 6)
x = 6

After 6 years it is (3x + 5), then after further 6 years, father's age = (3x +12) and daughter's age = (x + 12)
$$\frac{(3x+12)}{(x+12)}$$= ?

Substitute the value of x, we get
$$\frac{30}{18}$$=1.6
After further 6 years, father will be 1.6 times of daughter's age.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 10 / 22

A father said his son, "I was as old as you are at present at the time of your birth." If the father age is 40 now, the son age 5 years back was:
Let the son's present age be x years.
Then, (40 - x) = x
=> x= 20.
Son's age 5 years back = (20 - 5) = 15 years.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 11 / 22

The sum of the present ages of a father and his son is 60 years. five years ago, the father's age was four times the age of the son. so now the son's age will be:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 5= 4(x - 5)
55 - x = 4x - 20
5x = 75
Thus,
=> x = 15
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 12 / 22

The ratio of the present ages of A and B is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages
let their present ages be 3X and 4X.
5 years ago, the ratio of their ages was 5 : 7,
Thus, (3x-5) : (4x-5) = 5 : 7.
Solving, we get X = 10.
Hence, their present ages are 3X = 30 and 4X = 40
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 13 / 22

Proportion of Dhoni's age to Ganguly's age is 4:3. Dhoni willl be 26 years old after 6 years. What is the age of Ganguly now?
Let the present ages of Dhoni= 4x and Ganguly = 3x
So, 4x + 6 = 26
x = 5
Now,
Present age of Ganguly = 3x
So,
=> 3*5 = 15 years.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 14 / 22

Riya's age after 20 years will be 5 times his age 4 years back. What is the present age of Riya?
Let Riya's present age be x years.
Riya's age after 20 years = (x + 20) years.
Riya's age 4 years back = (x - 4) years
Then,
x + 20 = 5 (x - 4)
x + 20 = 5x - 20
=> x = 10 Ans.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 15 / 22

The ages of A,B and C together are 60 years. B is 4 times as old as A and C is 12 years older than A. Then, the respective age of A,B and C is?
Let A's age = X
Now,
C is 12 yrs older than A
So, C's age = x+12
B is 4 times as old as A
so B's age = 4x
The ages of A,B and C together are 57 years
x + (x+12) + 4x = 60
=> 6x = 48
x = 8
Thus,
A's age = 8
B's age = 4x= 32
C's age = x+12=20 Ans.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 16 / 22

The average age of 80 boys in a class is 15. The average age of group of 15 boys in the class is 16 and the average of another 25 boys in the class is 14. What is the average age of the remaining boys in the class?
Average age of 80 boys = 15 x 80 = 1200 yrs.-----(i)
average age of 15 boys = 15 *16 = 240 yrs-----(ii)
average age of 25 boys = 14 * 25 = 350 yrs.-----(iii)
Remaining boys= 80-(15+25)= 40 boys
Average age of remaining 40 boys =
$$\frac{1200 - (240+350)}{80 - (25+15)}$$
= $$\frac{610}{41}$$
= 15.25 years. Ans.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 17 / 22

When Ram was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Ram's brother is 6 years older than Ram and his mother is 3 years younger than his father, how old was Ram's sister when Ram was born?
Ram age when he was born = 0 years
=> His brother's age = 6 year
=> His father's age = brother age + 32years
= 6+32 = 38
=> His mother's age = father's age – 3
=38-3 = 35
So sister's age = 35-25 = 10 years. Ans.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 18 / 22

Six years ago Rahul was X times as old as Rishi was. If Rahul is now 17 years old, how old is Rishi now in terms of X?
Let Rishi's age now be A
Rahul's age= B
(A - 6) = X(B - 6)
But Rahul is 17 and therefore (17-6)=11 = X(B - 6)
$$\frac{11}{X}$$ = B-6
$$\frac{11}{X}$$ + 6 = B
B = $$\frac{11}{X}$$ + 6 Ans.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 19 / 22

Paul is 2 years elder than Peter. After 6 years the total of their ages will be 7 times of their current age. Then the age of Paul is:
Let Peter's age = x.
Then Paul's age = x + 2
After 6 years the total of their ages will be 7 times of their current age.
Not clear.
So the given data are inadequate. Ans.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 20 / 22

Ravi got married 10 years ago. His present age is $$\frac{6}{5}$$ times his age at the time of his marriage Ravi's sister was 5 years younger to him at the time of his marriage. The present age of Ravi's sister is ?
Let Ravi's age at the time of his marriage = X years
Then,
=> X + 10 = $$\frac{6}{5}$$ X
X = 50.
Since got married 10 years ago,
So, his present age = 50+10= 60
His sister is 5 years younger => 60-5 = 55 years. Ans.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 21 / 22

If 6 years are subtracted from the present age of Ram and the remainder is divided by 18, then the present age of his grandson Rahul is obtained. If Rahul is 2 years younger to Rishi whose age is 5 years, then what is the age of Ram ?
Let the Present age of Ram = x
Rahul's age = 5-2 = 3
So, as per the question:
$$\frac{x-6}{18}$$ = 3
x-6 = 54
x = 60
Ram's present age = 60 years Ans.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA

Example 22 / 22

The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
As per given in question:
(A+B)=12+(B+C)-----(i)
So,
(A+B) - (B+C)= 12
A-C= 12
Thus;
C is younger than A by 12 years.
Ans.
If the current age of a person be y, then

- age after n years = y+ n
- age n years ago = y – n
- n times the age = ny
- If ages in the numerical are mentioned in ratio A : B, then A : B will be Ay and By
NA
NA