Ages

How to Solve Problems on Ages?

To make this easier for you, let’s take a look at some of the basic mathematical concepts and tricks related to problems on ages:

  • If the present age of a person is X, then
    • Age after n years = X + n
    • Age n years ago = X – n
    • n times the present age = nX
    • If ages in the numerical are mentioned in the ratio A:B, then A:B will be AX and BX
  • If the sum of ages is X and Y and the ratio of their ages is p:q respectively, then you can determine the age of Y by using the formula shown below:
    • Age of Y = Ratio of Y/ Sum of ratios x sum of ages
    • Age of Y = q/ (p+q) x A

Points to Remember

  • After reading the problems on ages, assume the unknown age to be some variable, let’s say ‘X’.
  • Convert the statements in the question into mathematical equations.
  • Calculate the variable by solving the equations and the obtained value must satisfy the conditions given in the problem.

Important Formulas

Here are a few formulas linked to age problems that may help you answer the questions faster and acquire a better understanding of the concept:

  • If you are assuming the current age to be x, then the age after n years will be (x+n) years.
  • If you are assuming the current age to be x, then the age before n years will be (x-n) years.
  • If the age is given in the form of a ratio, for example, p:q, then the age shall be considered as qx and px
  • If you are assuming the current age to be x, then n times the current age will be (x×n) years
  • If you are assuming the current age to be x, then 1/n of the age shall be equal to (x/n) years