Question

Present ages of Aahna and Vaibhav are in the ratio 3 : 5 . Nine years from now the ratio of their ages was be 4 : 5 . Find their present ages.

Answer 1

Answer:

★ Aahna's age = 5.4 years

★ Vaibhav's age = 9 years

Step-by-step explanation:

Let

• Present age of Aahna be 3x and
• Present age of Vaibhav be 5x.

After 9 years,

• Aahna's age = (3x + 9)
• Vaibhav's age = (5x + 9)

According to the Question;

The ratio of their ages after 9 years = 4:5

$\sf{\dfrac{3x+9}{5x+9}=\dfrac{4}{5}}$

On cross multiplication,

⇒ 5 (3x + 9) = 4 (5x + 9)

⇒ 15x + 45 = 20x + 36

⇒ 45 - 36 = 20x - 15x

⇒ 9 = 5x

⇒ x = 9/5

For finding present ages,

• Aahna's age = 3x = 27/5 = 5.4 years
• Vaibhav's age = 5x = 9/5 × 5 = 9 years

Hence,

• Aahna's age = 5.4 years
• Vaibhav's age = 9 years

Answer 2

$\purple\bigstar\huge\tt{QUESTION:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

Present ages of Aahna and Vaibhav are in the ratio 3 : 5 . Nine years from now the ratio of their ages was be 4 : 5 . Find their present ages.

$\: \: \: \: \: \: \: \: \: \: \: \:$

$\purple\bigstar\huge\tt{SOLUTION:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

First we understand the wordings of question. Then we make equation out of this.

So in First line it says Present age of Aahan and Vaibhav are in the ratio 3:5

So the equation become is :-

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt\purple{ Present \: age \: of \: Aahan = 3x}$

$\tt\purple{ Present \: age \: of \: vaibhav \: = 5x }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

Now in second line it says Nine years from now (Nine years later) the age of both aahan and vaibhav

After Nine years (So +5 in both ages)

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt\purple{After \: Nine \: years \: Aahan \: age = 3x + 9}$

$\tt\purple{After \: Nine \: years \: Vaibhav \: age = 5x + 9}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

The ratio of their ages was be 4 : 5 means there age became 4 divide by 5

So the whole equation becomes

$\: \: \: \: \: \: \: \: \: \: \: \:$

$\purple \rightarrow \tt{ \frac{3x + 9}{5x + 9} = \frac{4}{5} }$

$\purple\bigstar \tt{Now \: solve \: the \: ques}$

$\: \: \: \: \: \: \: \: \: \: \: \:$

$\purple \rightarrow \tt{ \frac{3x + 9}{5x + 9} = \frac{4}{5} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\small\tt\purple{Do \: cross \: multiplication}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple \rightarrow \small\tt{ 5(3x + 9) = 4(5x + 9) }$

$\purple \rightarrow \small\tt{ 15x + 45 = 20x + 36}$

$\purple \rightarrow \small\tt{ 15x - 20x = 36 - 45}$

$\purple \rightarrow \small\tt{ - 5x = - 9}$

$\purple \rightarrow \small\tt{ \cancel - 5x = \cancel - 9}$

$\purple \rightarrow\tt{ x = \frac{9}{5} }$

$\purple \rightarrow\tt{ x = \frac{ \cancel9}{ \cancel5} }$

$\small \boxed{ \purple \rightarrow\tt{\underline x = \: 1.8 }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\small\tt\purple{ Present \: age \: of \: Aahan = 3x}$

$\small\tt\purple{ Present \: age \: of \: Aahan = 3 \times 1.8}$

$\small\tt\purple{ Present \: age \: of \: Aahan = 5.4}$

$\small\tt\purple{ Present \: age \: of \: Aahan = 5years \: 4months}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\small\tt\purple{ Present \: age \: of \: vaibhav \: = 5x }$

$\small\tt\purple{ Present \: age \: of \: vaibhav \: = 5 \times 1.8 }$

$\small\tt\purple{ Present \: age \: of \: vaibhav \: = 9.0 }$

$\small\tt\purple{ Present \: age \: of \: vaibhav \: = 9years }$