Question

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

Answer 1

⇝ Appropriate Question :-

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

⇝ Given :-

• Amit is 19 Years younger than his cousin.

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

⇝ To Find :-

• Their Present Ages.

⇝ Solution :-

Let

• Present Age of Amit = x years

So

• Present Age of Cousin = (x + 19) years.

❒ After 5 Years ;

• Age of Amit = (x + 5) years

• Age of Cousin = (x + 24) years

⏩ According To Question :

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

$:\longmapsto \rm 3(x + 5) = 2(x + 24)$

$:\longmapsto \rm 3x + 15 = 2x + 48$

$:\longmapsto \rm 3x - 2x = 48 - 15$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 33} }}}$

So,

• Age of Amit = $\rm x$ = 33 years

• Age of Cousin = $\rm x$ + 19 = 33 + 19 = 52 years

Hence,

$\small\pink{\begin{cases} \bf Present  \:Age  \: of  \: Amit = 33 \:years \\  \\  \bf Present \:  Age \:  of \:  Cousin = 52 \: years\end{cases}}$

Answer 2

Answer:

Given :-

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

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(Amit)} =\: a\: years$

$\mapsto \bf Present\: Age_{(Cousin)} =\: (a + 19)\: years$

❒ After 5 years their ages will be :

◘ Age Of Amit :

$\leadsto \sf\bold{\green{Age_{(Amit)} =\: (a + 5)\: years}}$

◘ Age Of Cousin :

$\leadsto \sf Age_{(Cousin)} =\: (a + 19 + 5)\: years$

$\leadsto \sf\bold{\green{Age_{(Cousin)} =\: (a + 24)\: years}}$

According to the question,

$\bigstar$ After 5 years, their ages will be in the ratio of 2 : 3.

$\implies \bf \bigg\{\dfrac{Age\: Of\: Amit}{Age\: Of\: Cousin}\bigg\} =\: \bigg\{\dfrac{2}{3}\bigg\}$

$\implies \sf \dfrac{a + 5}{a + 24} =\: \dfrac{2}{3}$

By doing cross multiplication we get,

$\implies \sf 2(a + 24) =\: 3(a + 5)$

$\implies \sf 2a + 48 =\: 3a + 15$

$\implies \sf 2a - 3a =\: 15 - 48$

$\implies \sf {\cancel{-}} a =\: {\cancel{-}} 33$

$\implies \sf\bold{\purple{a =\: 33}}$

Hence, their required present ages are :

❒ Present Age Of Amit :

$\longrightarrow \sf Present\: Age_{(Amit)} =\: a\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Amit)} =\: 33\: years}}$

❒ Present Age Of Cousin :

$\longrightarrow \sf Present\: Age_{(Cousin)} =\: (a + 19)\: years$

$\longrightarrow \sf Present\: Age_{(Cousin)} =\: (33 + 19)\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Cousin)} =\: 52\: years}}$

${\footnotesize{\bold{\underline{\therefore\: The\: present\: age\: of\: Amit\: and\: his\: cousin\: is\: 33\: years\: and\: 52\: years\: .}}}}$

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★ VERIFICATION ★

$\leadsto \sf \dfrac{a + 5}{a + 24} =\: \dfrac{2}{3}$

By putting the value of a = 33 we get,

$\leadsto \sf \dfrac{33 + 5}{33 + 24} =\: \dfrac{2}{3}$

$\leadsto \sf \dfrac{\cancel{38}}{\cancel{57}} =\: \dfrac{2}{3}$

$\leadsto \bf \dfrac{2}{3} =\: \dfrac{2}{3}$

Hence, Verified.