# Formulas For Ages

## 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.

## Basic 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