Important Formula: Problem on Ages

Important 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 1/n of age is x/n.

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 years.
and, B's current age 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;

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;

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;

Concept 5

The ratio of the present ages of A and B is p: q and after t years, it becomes r: s, then;

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;

Examples

Q1: Amitabh said to his friend "If you subtract 18 from my age the two digits of my age will reverse their positions. Also my age is six, less than 8 times the sum of digits of my age". Find Amitabh's age.
(a) 46 years 
(b) 37 years 
(c) 56 years 
(d) 42 years
Ans: (d)
Sol: Let Mayank's age be (10x + y) years
Age by reversing the digits = (10y + x) yrs
Now, 10x + y - 18= 10y + x
9x - 9y = 18
x - y = 2..................(1)
Also,
10x+y = 8(x+y) - 6
2x - 7y = -6............. (2)
Solving equations (1) and (2),
x = 4 , y = 2
Therefore, Mayank's age = 10x + y
= 10(4) + 2
= 42 years