Question

A father is eight times as old as his son . In 10 years , he will be three times as old as his son . The age of son is

Answer 1

Answer:

The age of son is 4 years

Step-by-step explanation:

Let,

Son's age = x

Father's age = 8x

In 10 years,

Son's age = x + 10

Father's age = 8x + 10

Also,

Father's age will be three times as old as his son

So,

⇒ 3 (x + 10) = 8x + 10

⇒ 3x + 30 = 8x + 10

⇒ 3x - 8x = 10 - 30

⇒ - 5x = - 20

⇒ 5x = 20

⇒ x = 20 / 5

⇒ x = 4

Therefore,

The age of son is 4 years

Verification:

★ Value of 8x :

⇒ x = 4

⇒ 8 (4)

⇒ 8 × 4

⇒ 32

Father's age = 32 years

In 10 years,

Father's age will be three times as old as his son :

⇒ 4 + 10 = 14

⇒ 32 + 10 = 42

⇒ 42 /14 = 3

Answer 2

$\bigstar$ $\sf{\red{\underline{\underline{\purple{To\:Find:-}}}}}$

• The Age of Son .

$\bigstar$ $\sf{\purple{\underline{\underline{\red{SOLUTION:-}}}}}$

♻️ GIVEN :-

• A father is 8times as old as his son
• In 10 years , father will be 3times as old as his son .

☞ Suppose,

• Age of Son = “x” years

• And Age of Father = “y” years

☞ initially,

• Age of Son = “x” years

• So, Age of Father = “8x” years

☞ In 10 years,

• Age of son = (10 + x) years
• And Age of Father = (10 + y) years

☞ GIVEN THAT,

• Age of Son = (10 + x) years

• So, Age of Father = 3(10 + x) years

♻️ CALCULATION :-

☞ According to question, Initially

• y = 8x ------(1)

☞ According to question, In 10 years

• Age of Father = 3 (Age of son)

$\tt{\implies\:(10\:+\:y)=\:3\times(10\:+\:x)\:}$

☞ Putting the value “y = 8x” in the above equation,

$\tt{\implies\:(10\:+\:8x)\:=\:(30\:+\:3x)\:}$

$\tt{\implies\:5x\:=\:20\:}$

$\tt{\implies\:x\:=\:4\:}$

☞ Therefore, the age of Son is “4 years” .

$\bigstar\:\underline{\boxed{\bf{\red{Required\:Answer\::\:The\:Age\:of\:Son\:is\:\:4\:years\:}}}}$