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 be ax and 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

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