# Important Formulas – Age

Important Formulas on “Problems on Ages” :

1. If the current age is x, then n times the age is nx.

2. If the current age is x, then age n years later/hence = x + n.

3. If the current age is x, then age n years ago = x – n.

4. The ages in a ratio a : b will be ax and bx.

## Change of Ratio between Two Numbers

Suppose two numbers are in the ratio  and when a number  is added to each of these numbers, the ratio between them changes to

Then, we can define  as follows, which when multiplied by  and  gives the initial numbers.

Note: if  is subtracted from each of the numbers, use same formula with

### Proof

Let the numbers be  and

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