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# 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

- If the present age is
*x*, then*n*times the age is.**nx** - If the present age is
*x*, then age*n*years later/hence =**x + n.** - If the present age is
*x*, then age*n*years ago =*x*–*n*. - The ages in a ratio
*a*:*b*will beand*ax*.*bx* - 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

**Read Also: Tips And Tricks to solve Problem On Ages Questions**

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