Question

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

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

Age of Amit

= p years

Hence,

$\textbf{\underline{Age\;of\;Amit\;Cousin}}$

= (p + 19) years

$\textbf{\underline{Age\;of\;Amit\;after\;5\;years}}$

= (p + 5) years

$\textbf{\underline{Age\;of\;Amit\;Cousin\;after\;5\;years}}$

= (p + 19 + 5) years

= (p + 24) years

$\textbf{\underline{Ratio\;after\;5\;years}}$

= 2 : 3

Therefore,

$\tt{\rightarrow\dfrac{p+5}{p+24}=\dfrac{2}{3}}$

3 × (p + 5) = 2 × (p + 24)

3p + 15 = 2p + 48

3p - 2p = 48 - 15

p = 33

Hence,

$\textbf{\underline{Age\;of\;Amit\;=33\;years}}$

$\textbf{\underline{Present\;Age\;of\;Amit\;Cousin}}$

= 33 + 19

= 52 years

Answer 2

Ⓖⓘⓥⓔⓝ :-

Raju is 19 years younger than his cousin.

ratios of their ages after 5 years = 2:3

Ⓕⓘⓝⓓ :-

THEIR PRESENT AGES ?

Ⓢⓞⓛⓤⓣⓘⓞⓝ  :-

Let age of cousin be x years

$\therefore$ Age of Raju = x-19 years

After 5 years

Age of cousin = x+5 years

Age of Raju = x - 19 + 5 = x - 14 years

ACCORDING TO QUESTION

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

$= 3 \times ( x - 14) = 2( x+ 5)$

$= > 3x - 42 = 2x + 10$

$collect \: like \: terms$

$= > 3x - 2x = 10 + 42$

$x = 52$

So, Present age of:

cousin = x = 52 years

Raju = x -19 = 52 - 19 = 33 years

$so, \: cousin \: present \: age \underline{ \boxed{52 \: years}}$

$and \: Raju\: present \: age \underline{ \boxed{33 \: years}}$