Question

Ava and liam's ages are currently in ratio 4:5 respectively. After 5 years, their ages will be in ratio 5:6. What is the current age of ava now?

Answer 1

Answer:

$\textbf{The current age of Ava is 20 years}$

Step-by-step explanation:

Ava and liam's ages are currently in ratio 4:5 respectively. After 5 years, their ages will be in ratio 5:6. What is the current age of ava now?

$\text{Let the ages Ava and Liam be x and y}$

Given:

$\text{x:y=4:5}$

$\text{Then, x=4k and y=5k}$

$\text{After 5 years,}$

$\text{(4k+5):(5k+5)=5:6}$

$\frac{4k+5}{5k+5}=\frac{5}{6}$

$\implies\:6(4k+5)=5(5k+5)$

$\implies\:24k+30=25k+25$

$\implies\:k=5$

$\therefore\:\text{The current age of Ava is 20 years}$