Question

Amit is 19 years younger than his cousin. After 5 years, their ages will be in the ratio 2:3. Find their present ages.​

Answer 1

✬ Amit = 33 Years ✬

✬ Cousin = 52 Years ✬

Step-by-step explanation:

Given:

• Amit is 19 years younger than his cousin.
• After 5 years their ages will be in ratio 2 : 3.

To Find:

• What are their present ages ?

Solution: Let Amit's present age be x years. Therefore,

➟ His cousin age = (x + 19) years

[ 5 years their ages will be ]

• Amit's age = (x + 5) years
• Cousin's age = (x + 19 + 5) years

A/q

• After 5 years their ages will be in ratio 2 : 3.

$\implies{\rm }$ (x + 5) : (x + 19 + 5) = 2 : 3

$\implies{\rm }$ x + 5/x + 24 = 2/3

$\implies{\rm }$ 3(x + 5) = 2(x + 24)

$\implies{\rm }$ 3x + 15 = 2x + 48

$\implies{\rm }$ 3x – 2x = 48 – 15

$\implies{\rm }$ x = 33

So, Present age of

➮ Amit is x = 33 years

➮ His cousin is 33 + 19 = 52 years

Answer 2

ᎯᏁᏕᏯᎬᏒ

Let the cousin's age be x years.

So, Amit's age = x-19 years.

After 5 years:-

Cousin's age = x+5 years.

Amit's age = x-14 years.

After 5 years, their ages will be in the ratio 2:3.

$\boxed{\rm{\purple{\frac{x - 14}{x + 5} = \frac{2}{3}}}}$

$\rm ➟ \: 3(x - 14) = 2(x + 5)$

$\rm ➟ \: 3x - 42 = 2x + 10$

$\rm ➟ \: 3x - 2x = 10 + 42$

$\rm \therefore \: \red{x = 52}$

His cousin's peresent age = 52 years.

Amit's present age = 33 years.