Question

raju is 19 years younger than his cousin . after five years, their ages will be in the ratio 2:3 . find their present ages.​

Answer 1

Solution :-

Let :-

Present age of Raju = x

Present age of cousin = y

After 5 years :-

Age of Raju = x + 5

Age of cousin = y + 5

According to the first condition :-

$\longrightarrow \sf x = y - 19 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ....................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+5}{y+5} = \dfrac{2}{3} \\\\\longrightarrow 3(x+5)= 2(y+5) \\\\\longrightarrow 3x+15 = 2y+10 \\\\\longrightarrow 3x-2y = -5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ....................(2)$

Substitute the value of x in eq (2) :-

$\longrightarrow \sf 3(y-19)-2y = -5 \\\\\longrightarrow 3y-57 - 2y = -5 \\\\\longrightarrow 3y-2y = -5+57 \\\\\longrightarrow \bf y = 52$

Substitute y = 52 in eq (1) :-

$\longrightarrow \sf x = 52 - 19 \\\\\longrightarrow \bf x = 33$

Present age of Raj = 33 years

Present age of cousin = 52 years

Answer 2

Answer:

Given :-

• Raju age is 19 years younger than his cousin.
• After five years their age will be in the ratio of 2:3.

To Find :-

• What is their present age.

Solution :-

Let, the present age of Raju be x

And, the present age of Raju's cousin be y

After 5 years,

Raju's age is x + 5

And, his cousin is 19 + x + 5 = 24 + x

Ratio of their age = 2:3

According to the question,

⇒ $\dfrac{x + 5}{24 + x}$ = $\dfrac{2}{3}$

⇒ 3(x + 5) = 2(24 + x)

⇒ 3x + 15 = 48 + 2x

⇒ 3x - 2x = 48 - 15

⇒ x = 33

Hence, the required ages,

Present age of Raju's is = x = 33 years

And, present age of his cousin = 19 + x = 19 + 33 = 52 years