**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?

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 38:**

* 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 – 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.

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

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