Question

Ram is half of his father age . Twenty years ago the age of father was six times the age of ram.find the age of ram and his father.

Answer 1

$\mathfrak{Step-By-Step\:Explanation:}$

Let the age of Ram be x years.

So his father's age :

$\tt{=2\times x}\\\\\\\tt{=2x\:years.}$

20 years ago,

• Ram's age was = (x - 20) years.
• His father's age was = (2x - 20) years.

According to question ,

$\implies\bold{6(x-20)=2x-20}\\\\\\\implies\bold{6x-120=2x-20}\\\\\\\implies\bold{6x-2x=120-20}\\\\\\\implies\bold{4x=100}\\\\\\\implies\bold{x=\dfrac{100}{4}}\\\\\\\implies\bold{x=25.}\\\\\\\boxed{\boxed{\bold{Ram's\:age=25\:years\:\&\:his\:father's\:age=50\:years.}}}$

Answer 2

Let the age of Ram's father be x.

Since Ram's age is half than his father's age so age of Ram is x/2.

20 years ago age of Ram and his father will be x/2 - 20 and x - 20 respectively.

Question says that age of Father will 6 times than the age of Ram therefore,

$\Longrightarrow \bold{ x - 20 = 6 ( \frac{x}{2} - 20 )} \\ \\ \Longrightarrow \bold{ x - 20 = 6(\frac{x}{2}) - 6(20)}$

⇒x - 20 = 3x - 120

⇒- 20 + 120 = 3x - x

⇒100 = 2x

⇒100/2 = x

50 years = Ram's father age

Since age of Ram is half of his father's age.

⇒ Age of Ram = 50/2 years

25 years = Ram's age