Question

$\huge\mathfrak\red {Question!}$
the present age of two children are in the ratio 2: 3 ...5 years ago the ratio of their ages was 1 : 2 find the present age ​

Answer 1

$\huge{\underline{\mathcal{\red{A}\green{n}\pink{s}\orange{w}\blue{e}\pink{R:-}}}}$

$\large\underline\bold\red{Given:-}$

The present age of two children are in the ratio of 2 : 3.

5 years ago the ratio of their ages was 1 : 2.

$\large\underline\bold\red{To\:Find:-}$

What is their present ages.

$\large\underline\bold\red{Solution:-}$

Let,

$\mapsto \bf Present\: Age_{(First\: Child)} =\: 2x\: years$

$\mapsto \bf Present\: Age_{(Second\: Child)} =\: 3x\: years$

❒ 5 years ago their ages will be :

$\leadsto \sf Age\: of\: First\: Child =\: (2x - 5)\: years$

$\leadsto \sf Age\: of\: Second\: Child =\: (3x - 5)\: years$

According to the question,

$\implies \bf (2x - 5) : (3x - 5) =\: 1 : 2$

$\implies \sf \dfrac{(2x - 5)}{(3x - 5)} =\: \dfrac{1}{2}$

By doing cross multiplication we get,

$\implies \sf 2(2x - 5) =\: 1(3x - 5)$

$\implies \sf 4x - 10 =\: 3x - 5$

$\implies \sf 4x - 3x =\: - 5 + 10$

$\implies \sf\bold{\purple{x =\: 5}}$

Hence, their present ages are :

❒ Present Age Of First Child :

$\longrightarrow \sf Present\: Age_{(First\: Child)} =\: 2x\: years$

$\longrightarrow \sf Present\: Age_{(First\: Child)} =\: 2 \times 5\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(First\: Child)} =\: 10\: years}}$

❒ Present Age Of Second Child :

$\longrightarrow \sf Present\: Age_{(Second\: Child)} =\: 3x\: years$

$\longrightarrow \sf Present\: Age_{(Second\: Child)} =\: 3 \times 5\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Second\: Child)} =\: 15\: years}}$ .

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