# Formulas For Ages

## Formulas For Problem on Ages

Here on this page you will get to know about the Formulas For Ages. These type of Formulas are widely used in the Problem on Ages questions and are beneficial for solving the question in exams Quickly and Efficiently.

## Important Formulas on Ages

1. If the present age is x, then n times the age is nx.
2. If the present age is x, then age n years later/hence = x + n.
3. If the present age is x, then age n years ago = x – n.
4. The ages in a ratio a : b will be ax and bx.
5. If the present age is x, then $\frac{1}{n} \$ of age is $\frac{x}{n} \$

## Important  Concepts on Problems on Ages

### Concept 1

x years ago the age of A was n1 times the age of B, and at present A’s age is n2 times that of B, then;
A’s current =$\frac{\left ( n_{1} -1\right )n_{2}x}{n_{1}-n_{2}}$ years.
and, B’s current age = $\frac{\left ( n_{1} -1\right )x}{(n_{1}-n_{2})}$years.

### Concept 2

The present age of A is n1 times the present age of B. After x years, age of A becomes n2 times the age of B, then;
A’s current = $\frac{\left ( n_{2} -1\right )n_{2}x}{(n_{1}-n_{2})}$ years.
and, B’s current age =$\frac{\left ( n_{2} -1\right )x}{(n_{1}-n_{2})}$ years.

### Concept 3

t1 years ago, the age of A was X times the age of B and after t2 years age of A becomes Y times the age of B, then;
A’s present age =$\frac{\left (x)(t_{1}+ t_{2}\right )( y – 1)}{(x-y)} + t_{1}$years
And B’s present age = $\frac{t_{2}(y – 1)+t_{1}(x – 1)}{x – y}$years

### Concept 4

The sum of present ages of A and B is X years, t years after, the age of A becomes Y times the age of B, then;
A’s present age =$\frac{xy + t(y-1)}{y +1}$years
And B’s present age= $\frac{x- t(y-1)}{y+1}$ years

### Concept 5

The ratio of the present ages of A and B is p: q and after t years, it becomes r: s, then;
A’s present age = $\frac{pt(r-s)}{ps-qr}$ years.
And, B’s present age = $\frac{qt(r-s)}{ps-qr}$ years

### Concept 6

The sum of present ages of A and B is X years, t years ago, the age of A was Y times the age of B, then;
Present age of A =$\frac{xy + t(y-1)}{y+1}$years
And, the present age of B = $\frac{x + t(y-1)}{y+1}$years

Question 1: Saina Nehwal is 8 years older than her cousin. Her cousin is 24 years younger than his mother. If the ratio between the ages of Saina and her cousin’s mother is 7 : 11. What will be the age of Saina’s cousin after 3 years?

A. 21 years
B. 20 years
C. 26 years
D. 23 years

Let the age of Saina = x, her cousin’s age = x – 8, Cousin’s mother age = x – 8 + 24
Ratio between the ages of Saina and her cousin’s mother is 7 : 11
x : x + 16 = 7 : 11
11 × x = (x + 16) × 7
11x = 7x + 112
4x = 112
x = 28
Saina’s cousin age = 28 – 8 = 20
After 3 years Saina’s cousin age = 20 + 3 = 23 years

Question 2 : Tiger’s present age is acquired, if we subtract 9 years from Arav’s present age and divide the remainder by 14. If Mohan’s age is 8 years and he is 3 years elder to Arav, then find Tiger’s present age.

A. 42
B. 79
C. 77
D. 85

Explanation:
Let Tiger’s present age be x
Given, Mohan’s present age 8 years
Then, Arav’s present age = 8-3 = 5 years
Given, if we subtract 9 years from Arav’s present age and divide the remainder by 14 we will get Tiger’s present age
= x-9/14 = 5
x-9 = 70
x = 79 years
Tiger’s present is 79 years

Question 3 : Erika was five times older than Gigi ten years ago. The age of an Erika will be twice that of a Gigi in five years. How old were Erika’s compared to Gigi five years ago?

A. 5:1
B. 3:1
C. 2:1
D. 4:1

Explanation :
Erika was 5 times older than Gigi 10 years ago.
Let the age of Gigi 10 years ago be x years.
∴ The age of Erika 10 years ago = 5x years
5 years from now, Erika will be twice older than Gigi.
∴ We can write now,
(5x + 10 + 5) = 2 × (x + 10 + 5)
⇒ 5x + 15 = 2x + 30
⇒ 3x = 15
⇒ x = 5
∴ Age of Gigi 10 years ago = 5 years
And, the age of Erika 10 years ago = 5x = 5 × 5 = 25 years
∴ The reqd. ratio $= \frac{25 + 5}{5+5} = \frac{30}{10} = 3:1$

Question 4 : Sum of the ages of Tendulkar and Dravid 16 years hence will be equal to 3 times their present age. If at present Tendulkar is 10 years elder to Dravid, then what are their present ages?

A. 22, 8
B. 29, 12
C. 13, 3
D. 13, 6

Let the present ages of Tendulkar and Dravid be x years and y years respectively.
As per the question,
(x + 16) + (y + 16) = 3(x + y)
x + y + 32 = 3x + 3y
x + y = 16 …..(i)
Also,
y + 10 = x
x – y = 10 …..(ii)
Solving eqns (i) and (ii), we get
x = 13 and y = 3
Therefore, Present ages of Tendulkar and Dravid is 13 years and 3 years respectively.

Question 5 : Amitabh said to his friend “If you subtract 18 from my age the two digits of my age will reverse their positions. Also my age is six, less than 8 times the sum of digits of my age”. Find Amitabh’s age.

A. 46 years
B. 37 years
C. 56 years
D. 42 years

Let Mayank’s age be (10x + y) years
Age by reversing the digits = (10y + x) yrs
Now, 10x + y − 18= 10y + x
9x – 9y = 18
x – y = 2………………(1)
Also,
10x+y = 8(x+y) – 6
2x – 7y = –6……….… (2)
Solving equations (1) and (2),
x = 4 , y = 2
Therefore, Mayank’s age = 10x + y
= 10(4) + 2
= 42 years

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