Question

The ratio of gaurav's and his brother's age are in the ratio 2:3. If the sum of their ages is 20, what is the present ages of them?​

Answer 1

Question :

The ratio of gaurav's and his brother's age are in the ratio 2:3. If the sum of their ages is 20, what is the present ages of them?

Answer :

$\sf\pink{Given:}$

• Ratio of Gaurav's and his brothers age is 2:3 .

• sum of their ages is 20 .

$\sf\pink{To\:find:}$

• Their present ages ?

Explanation :

• let their age be 2x and 3x .

By the given condition ,

$\\ \longrightarrow\sf{ 2x + 3x = 20}$

$\\ \longrightarrow\sf{ 5x = 20}$

$\\ \longrightarrow\sf{ x = \dfrac{20}{5}}$

$\\ \longrightarrow\sf{ x = 4}$

• Gaurav's age is 2x

$\\ \longrightarrow\sf{ 2\times 4}$

$\\ \longrightarrow\sf{ 8}$

Therefore the present age of Gaurav is 8 years .

• His brothers age is 3x

$\\ \longrightarrow\sf{ 3\times 4}$

$\\ \longrightarrow\sf{12}$

Therefore his brothers present age is 12 years .

Answer 2

⇒ Given:

The ratio of Gaurav's and his brother's age is 2:3.

The sum of their ages = 20

⇒ To Find:

Each of their ages.

⇒ Solution:

Let the age of Gaurav and his brother be 2x and 3x.

It is given that the sum of their ages is 20.

Forming an equation:

$\sf{2x+3x=20}$

Simplifying the equation:

$\sf{5x=20}$

$\sf{x=\dfrac{20}{5}}$

$\sf{x=4}$

Therefore:

Gaurav's age = 2x = 2 x 4 = 8 years

His brother's age = 3x = 3 x 4 = 12 years

∴ The age of Gaurav is 8 and the age of his brother is 12.

⇒ Verification:

We can write the ages we got in ratio format, after simplification, if we get the ratio mentioned in the question, our answer is correct.

= 8 : 12

Cancelling by 2:

= 4 : 6

Again cancelling by 2:

= 2 : 3

This is equal to the RHS.

LHS = RHS

Hence verified!