Question

Ava and Liam's ages are currently in a ration of 4:5 respectively. After 5 years, their ages would be in a ration of 5:6 respectively. What is Ava's current age?

Answer 1

Answer:

• Ava's current age is 20 years.

Step-by-step explanation:

Given that:

• Ava and Liam's ages are currently in a ratio of 4 : 5 respectively.
• After 5 years, their ages would be in a ratio of 5 : 6 respectively.

Let us suppose:

• Ava's current age be 4x years.
• Liam's current age be 5x years.

After 5 years ages will be:

• Ava's age = (4x + 5) years
• Liam's age = (5x + 5) years

To Find:

• What is Ava's current age?

Finding Ava's current age:

• According to the question.

⟶ (4x + 5)/(5x + 5) = 5/6

• Cross multiplication.

⟶ 6((4x + 5) = 5(5x + 5)

⟶ 24x + 30 = 25x + 25

⟶ 25x - 24x = 30 - 25

⟶ x = 5

∴ Ava's current age = 4x = (4 × 5) = 20 years

Answer 2

Answer:

Given :-

• Ava and Liam's ages are currently in a ratio of 4 : 5 respectively. After 5 years, their ages would be in a ratio of 5 : 6 respectively.

To Find :-

• What is the present age of Ava.

Solution :-

Let, the present age of Ava be 4x years

And, the present age of Liam will be 5x

$\leadsto$ $\sf\bold{\pink{After\: 5\: years\: :-}}$

Age of Ava be 4x + 5 years

And, the age of Liam will be 5x + 5 years

According to the question,

↦ $\sf \dfrac{4x + 5}{5x + 5} =\: \dfrac{5}{6}$

↦ $\sf 5(5x + 5) =\: 6(4x + 5)$

↦ $\sf 25x + 25 =\: 24x + 30$

↦ $\sf 25x - 24x =\: 30 - 25$

➦ $\sf\bold{\red{x =\: 5\: years}}$

Hence, the required present ages are :

✪ Present age of Ava :

⇒ $\sf 4x\: years$

⇒ $\sf 4(5)\: years$

⇒ $\sf 4 \times 5\: years$

➠ $\sf\bold{\purple{20\: years}}$

And,

✪ Present age of Liam :

⇒ $\sf 5x\: years$

⇒ $\sf 5(5)\: years$

⇒ $\sf 5 \times 5\: years$

➠ $\sf\bold{\purple{25\: years}}$

$\therefore$ The present age of Ava is 20 years.