All the concepts related to ages are discussed below with conditions and cases

Problems on ages are generally asked based on 3 situations

- Age some years ago.
- Present age.
- Age some years hence.

Any two of these above situations are given to find the third.

In some cases, the relation between the ages of two persons may also be given and in this case, simple linear equations are formed and their solutions are obtained.

**Formulas On Ages :**

1. Let t years ago the age of A was n1 times the of the age of B and at present, A’s age is n2 times the age of B then, *Present age of A is*

\begin{align*} \left[ \dfrac {n_{1}-1}{n_{1}-n_{2}}\right] \times n_{2}\times t \ \ years \end{align*}*the Present age of B*

\begin{align*} \left[ \dfrac {n_{1}-1}{n_{1}-n_{2}}\right] \times t \ years \end{align*}

2.let the present age of A is n1 times the present age of B.If t years hence the age of A would be n2 times of B then,

*Present age of A*

\begin{align*} \left[ \dfrac {n_{2}-1}{n_{1}-n_{2}}\right] \times n_{2}\times t \ years

\end{align*}*Present age of B*

\begin{align*} \left[ \dfrac {n_{2}-1}{n_{1}-n_{2}}\right] \times t \ years

\end{align*}

3. When the ratio of ages of A and B n years ago was x:y given now

*if their present age ratio is a:b then,*

\begin{align*} \dfrac {x+n}{y+n}=\dfrac {a}{b} \end{align*}*after m years their ratio of ages would be c:d then*,

\begin{align*} \dfrac {x+n+m}{y+n+m}=\dfrac {p}{q} \end{align*}

4. Let n years ago the ratio of ages of A, B and C are x:y:z then, *ratio of their present age is*

\begin{align*} \left( x+n\right) :\left( y+n\right) :\left( z+n\right) \end{align*}

5. Let n years hence the ratio of ages of A, B and C would be x:y:z then, *ratio of their present age is*

\begin{align*} \left( x-n\right) :\left( y-n\right) :\left( z-n\right) \end{align*}