Question

Two years ago, a man was five times as old as his son. Two years later his age will be 8 more than three times the age of the son. Find the present ages of man and his son.

Answer 1

Given :

• Two years ago, a man was five times as old as his son.
• Two years later his age will be 8 more than three times the age of the son.

To Find :

• The present age of man
• The present age of son

Solution :

Let the present age of man be x years.

Let the present age of son be y years.

Case 1 :

Two years ago man's age was five times older as age of his son.

Age of man 2 years ago, (x-2) years.

Age of son 2 years ago, (y-2) years.

Equation :

$\longrightarrow$ $\sf{(x-2) =5(y-2) }$

$\longrightarrow$ $\sf{x-2=5y-10}$

$\longrightarrow$ $\sf{x-5y=-10+2}$

$\longrightarrow$ $\sf{x-5y=-8}$

$\sf{x=-8+5y\:\:\:(1)}$

Case 2 :

After 2 years, man's age will be 8 more than 3 times the son's age.

Age of man, 2 years later, (x+2) years.

Age of son, 2 years later (y+2) years.

Equation :

$\longrightarrow$ $\sf{x+2=3(y+2)+8}$

$\longrightarrow$ $\sf{x+2=3y+6+8}$

$\longrightarrow$ $\sf{x+2=3y+14}$

$\longrightarrow$ $\sf{x-3y=14-2}$

$\longrightarrow$ $\sf{-8+5y-3y=12}$

$\longrightarrow$ $\sf{5y-3y=12+8}$

$\longrightarrow$ $\sf{2y=20}$

$\longrightarrow$ $\sf{y=\cancel\dfrac{20}{2}}$

$\longrightarrow$ $\sf{y=10}$

Substittute, y = 10 in equation (1),

$\longrightarrow$ $\sf{x=-8+5y}$

$\longrightarrow$ $\sf{x=-8+5(10)}$

$\longrightarrow$ $\sf{x=-8+50}$

$\longrightarrow$ $\sf{x=42}$

$\large{\boxed{\sf{\red{Present\:age\:of\:man\:=\:x\:=\:42\:years}}}}$

$\large{\boxed{\sf{\purple{Present\:age\:of\:son\:=\:y\:=\:10\:years}}}}$

Answer 2

Answer:

★ Son's age = 10 Years ★

★ Man's age = 42 Years ★

Step-by-step explanation:

Given:

• Two years ago , man was five times as old as his son.
• Two years later his age will be 8 more than three times the age of his son.

To Find:

• Present ages of man and his son.

Solution: Let the present age of father be x years and present age of son be y years.

★ Two years ago their ages was ★

• Man's age = (x – 2) Years
• Son's age = (y – 2) Years

A/q

$\small\implies{\sf }$ x – 2 = 5(y – 2)

$\small\implies{\sf }$ x – 2 = 5y – 10

$\small\implies{\sf }$ x = 5y – 10 + 2

$\small\implies{\sf }$ x = 5y – 8.......(1)

★ Two years hence their ages will be ★

• Man's age = (x + 2) Years
• Son's age = (y + 2) Years

A/q

$\small\implies{\tt }$ x + 2 = 8 + 3 (y + 2)

$\small\implies{\sf }$ x + 2 = 8 + 3y + 6

$\small\implies{\sf }$ 5y – 8 + 2 = 3y + 14 [ From equation 1 since, x = 5y – 8 ]

$\small\implies{\sf }$ 5y – 6 = 3y + 14

$\small\implies{\sf }$ 5y – 3y = 14 + 6

$\small\implies{\sf }$ 2y = 20

$\small\implies{\sf }$ y = 20/2

$\small\implies{\sf }$ y = 10

Hence, Present age of son is x = 10 Years and present age of man is x = 5y – 8

→ x = 5(10) – 8

→ x = 50 – 8

→ x = 42 Years.