# Formulas For Ages

## Formulas For Ages

These type of Formulas are widely used in the Problem on Ages questions. These formula are beneficial for solving the question in exams Quickly and Efficiently.

## Basic Formulas on Ages

1. If the present age is x, then n times the age is nx.
2. If the present age is x, then age n years later/hence = x + n.
3. If the present age is x, then age n years ago = x – n.
4. The ages in a ratio a : b will be ax and bx.
5. If the present age is x, then $\frac{1}{2} \$ of age is $\frac{x}{n} \$

## Ages Formulas and Concept on Problems on Ages

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 = (n1 – 1) / (n1 – n2) n2*x years.
and, B’s current age = (n1 – 1) / (n1 – n2) x years.

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 = (n2 – 1) / (n1 – n2) n2*x years.
and, B’s current age = (n2 – 1) / (n1 – n2) x years.

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 ={ X(t1+t2) (Y-1) }/ (X-Y) + t1 years
And B’s present age = {t2(Y-1)+ t1(X-1)} / (X-Y) years

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 = XY + t(Y-1)/ (Y+1) years
And B’s present age= X-t (Y-1)/ (Y+1) years

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 = pt(r-s)/(ps-qr) years.
And, B’s present age = qt(r-s)/ (ps-qr) years

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 = XY+t(Y-1)/(Y-1) years
And, the present age of B = X+t(Y-1)/(Y+1) years

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