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 $p_1:q_1$ and when a number $n$ is added to each of these numbers, the ratio between them changes to $p_2:q_2.$

Then, we can define $k$ as follows, which when multiplied by $p_1$ and $q_1$ gives the initial numbers.

Note: if $n$ is subtracted from each of the numbers, use same formula with $-\mathrm{n.}$

Proof

Let the numbers be $k{p}_1$ and $k{q}_1$

Difference and Ratio between Two Numbers

 

Proof

Sum and Ratio between Two Numbers

Proof

 

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