Shortcut - Problems on ages
One variable linear equation.
Question:
Age of father is twice that of son at present. After 5 years, sum of their ages will be 100. What is the present age of father?
Answer:Assume age of son = S
Age of father = 2S
Age of father after 5 years = 2S + 5
Age of son after 5 years = S + 5
Given,
(2S + 5) + (S + 5) = 100
3S + 10 = 100
S = 30
Present age of father = 2S = 60
Shortcut - Problems on ages
One variable quadratic equation.
Question:
Sum of the ages of father and son is 45. Product of their ages is 350. What is the difference between their ages?
Answer:Age of father = F;
Age of son = S
F + S = 45; F = 45 – S --- Equ (1)
F x S = 350 --- Equ (2)
Sub Equ (1) in (2)
(45 – S)S = 350
$45S – S^{2} = 350$
$S^{2} – 45S + 350 = 0$
By solving this quadratic equation, we get
S = 10, 35. (Neglect 35 since son’s age cannot be greater than father’s.)
From (1) Father’s age = 35
Difference between their ages = 35 -10 = 25
Formula to find roots of a quadratic equation:
A – Coefficient of $x^{2}$;
b - coefficient of x;
c – constant
Shortcut - Problems on ages
Simultaneous equations.
Question:
Sum of ages of father and son at present is 40. After 5 years the ratio between their ages become 7 : 3. Find the present ages of father and son.
Answer:Assume present age of father = F
Assume present age of son = S
Given, F + S = 40 --- Equ (1)
Father’s age after 5 years = F + 5
Son’s age after 5 years = S + 5
Given, (F + 5)/(S + 5) = 7/3, which gives
3F + 15 = 7S + 35
3F – 7S = 20 --- Equ (2)
By solving Equ (1) and (2), we get
Age of son, S = 10
Age of father, F = 30
Shortcut - Problems on ages
Solution using common factor ‘x’.
Question:
Age of MS and VK were in the ratio 4 : 3 five years back. Their ages will be in the ratio 5 : 4 in two years. Find their present ages.
Answer:Difference between the two compared years = 7.
Difference in ratio = 1
x = 7/1 = 7
Age of MS and VK 5 years ago = 4x and 3x
4x = 4(7) = 28
3x = 3(7) = 21
Age of MS at present = 28 + 5 = 34
Age of VK at present = 21 + 5 = 26
Note:
This method is applicable only when ‘d’ is equal on both sides.
The ratios can be modified to get ‘d’ same in both sides.