Question

Ram is half his father's age. Ten years ago he was one-third his father's age. What are their present ages?​

Answer 1

Given:

1. Ram's age is half his father's age.
2. 10 years ago, he was one-third his father's age.

Find:

• Their present ages.

Answer:

Let us assume Ram's father's present age to be x years.

Then Ram's present age is x/2 years.

10 years ago:

Ram's father's age will be x-10 years.

Ram's age will be x-10/3 years.

Also, Ram's age 10 years ago will be:

$\frac{x}{2} - 10=\frac{x-20}{2}$

$So, \: \frac{x-20}{2}=\frac{x-10}{3} \\ \\ \implies 3[x-20]=2[x-10]\\\implies 3x-60=2x-20\\\implies 3x-2x=60-20\\\implies x=40\\\therefore x=40,\frac{x}{2}=20.$

Answer 2

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\underline{\sf{\blue{Given:}}}}$

• Ram is half his father's age
• Ten years ago he was one-third his father's age.

$\bf{\underline{\sf{\blue{To\:find:}}}}$

• Present age of Rahul
• Present age of Father

$\bf{\underline{\sf{\blue{Solution:}}}}$

Let the present age of Father be x years.

As per first condition :-

• Ram is half his father's age

Present age of Ram = $\large\sf\frac{1}{2}$ × x

Present age of Ram = $\large\sf\frac{x}{2}$ years --->1

As per second condition :-

• Ten years ago he was one-third his father's age.

Ages 10 years ago :-

Father's age = x - 10 years

Ram's age = $\large\sf\frac{x}{2}$ - 10

Ram's age = $\large\sf\frac{x(1)\:-\:10(2)}{2}$

Ram's age = $\large\sf\frac{x-20}{2}$ years.

Representig it mathematically and solving further we will be able to simplify the condition.

$\bf\implies$ $\large\sf\frac{x-20}{2}$ = $\large\sf\frac{1}{3}$ × x - 10

$\bf\implies$ $\large\sf\frac{x-20}{2}$ = $\large\sf\frac{x-10}{3}$

$\bf\implies$ 3 ( x - 20) = 2 ( x - 10)

$\bf\implies$ 3x - 60 = 2x - 20

$\bf\implies$ 3x - 2x = -20 + 60

$\bf\implies$ x = 40

Substitute x = 40 in equation 1,

=> Present age of Ram = $\large\sf\frac{40}{2}$

Present age of Ram = 20 years

•°• Present age of Father = 40 years

Present age of Ram = 20 years.