Problems on Ages

x years ago the age of A was $n_1$ times the age of B, and at present A’s age is $n_2$ times that of B, then;

A’s current = $\frac{\left (x)(t_{1}+ t_{2}\right )( y – 1)}{(x-y)} + t_{1}$ years

and, B’s current age =$\frac{\left ( n_{1} -1\right )x}{(n_{1}-n_{2})}$

The present age of A is $n_1$ times the present age of B. After x years, age of A becomes $n_2$ times the age 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 =$\frac{\left ( n_{1} -1\right )x}{(n_{1}-n_{2})}$

$t_1$ years ago, the age of A was X times the age of B and after $t_2$ years age of A becomes Y times the age 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 =$\frac{t_{2}(y – 1)+t_{1}(x – 1)}{x – y}$

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 current = $\frac{xy + t(y-1)}{y +1}$ years

and, B’s current age =$\frac{x- t(y-1)}{y+1}$

The ratio of the present ages of A and B is p: q and after $t$ years, it becomes $r : s$, then;

A’s current = $\frac{pt(r-s)}{ps-qr}$ years

and, B’s current age =$\frac{qt(r-s)}{ps-qr}$

TThe 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;

A’s current = $\frac{xy + t(y-1)}{y +1}$ years

and, B’s current age =$\frac{x+ t(y-1)}{y+1}$