Important Formulas on "Problems on Ages"
1. If the current age is x, then n times the age is nx.
2. If the current age is x, then age n years later/hence = x + n.
3. If the current age is x, then age n years ago = x - n.
4. The ages in a ratio a : b will be ax and bx.
1
x
5. If the current age is x, then
of the age is .
n
n
Problems based on ages are generally asked in most of the competitive
examinations. To solve these problems, the knowledge of linear equations is
essential. In such problems, there may be three situations:
1.
2.
3.
Age some years ago
Present age
Age some years hence
Ex: The difference between the age of two persons ‘A’ & ‘B’ is 16 years, and
the age of ‘A’ is three times the age of ‘B’. Find the ratio of their ages after 6
years?
Sol:
A : B
3 : 1
Difference 2 = 16
1 = 8
A = 24 yrs B = 8 yrs
Ratio of their ages after 6 years
A : B = (24+6) : (8+6)
= 30
: 14
= 15
:
7
Ex: The sum of the age of father, mother and son is 96 years. After 8 years the
mother will be thrice as old as her son and the father will be as old as the
mother and son together. Find the present age of the mother?
Sol:
Sum ( F+ M + S)
= 96 Yrs
Sum (After 8 year) = 96 + 24
= 120 Yrs
F:M :S
4: 3: 1
Sum of the ages
Mother‘s age
8
3
= 120
= 45
mother’s Present age = 45 – 8
= 37 Yrs