# Shortcut of Problems on Ages

Shortcut 37:

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?
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 38:

Question:
Sum of the ages of father and son is 45. Product of their ages is 350. What is the difference between their ages?
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 – S2 = 350
S2 – 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

Shortcut 39:

Two Variable 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.
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

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