Formulas For Ages

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