Question

The ages of Aman and Arun are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages

Answer 1

Answer:

Aman's age = 20, Arun's age = 28

Step-by-step explanation:

Let $x$ = Aman's age

Let $y$ = Arun's age

- - - -

$x+4+y+4=56$ (Sum of their age is 56 after 4 years in the future)

$x+y+8=56$

$x+y=48$

$\frac{x}{y} = \frac{5}{7}$ (Ages are in the ratio 5:7)

$x=\frac{5}{7}y$

Now, we can use substitution to find for Arun's age:

$x+y=48$

$\frac{5}{7}y+y=48$

$\frac{12}{7}y=48$

$y=28$

∴ Arun is $28$

To find for Aman's age, we can use substitution:

$x+y=48$

$x+28=48$

$x=20$

∴ Aman is 20

Hope this helps :)