Question

pesent ages of anu and raj are in the ratio 4:5. eight years from now the ratio of thier ages will be 5:6. find thier present ages​

Answer 1

Ratio of present age of anu and raj is 4:5.

Ratio of their ages after 8 years is 5:6.

We have to find, Present age of both anu and raj.

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☯ Let their present age in the form of x.

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★ Ratio of present age of anu and raj is 4:5.

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Therefore,

• Present age of anu = 4x
• Present age of raj = 5x

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Their ages after 8 years

• Age of anu = 4x + 8
• Age of raj = 5x + 8

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★ Ratio of their age after 8 years is 5:6.

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Therefore,

$\underline{\bigstar\:\boldsymbol{According\:to\: Question\::}}$

$:\implies\sf \dfrac{4x + 8}{5x + 8} = \dfrac{5}{6}$

$:\implies\sf 6(4x + 8) = 5(5x + 8)$

$:\implies\sf 24x + 48 = 25x + 40$

$:\implies\sf 48 - 40 = 25x - 24x$

$:\implies{\underline{\boxed{\sf{\pink{x = 8}}}}}\;\bigstar$

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Therefore,

• Present age of anu, 4x = 4 × 8 = 32 years

• Present age of raj, 5x = 5 × 8 = 40 years

Answer 2

AnsWer :

$\sf Present\:Age \:\:\xrightarrow{After\:8\:Years} \:\:Future\:Age\\{\sf Anu : Raj \qquad \qquad \: \: \qquad\: Anu:Raj } \\{\sf 4 \::\:5 \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \qquad 5 : 6}$

Let the present age of Anu be 4x and Raj be 5x respectively.

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☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf \dfrac{Anu+8}{Raj+8}=\dfrac{5}{6}$

$:\implies\sf \dfrac{4x + 8}{5x + 8} = \dfrac{5}{6}$

$:\implies\sf (4x + 8) \times 6= 5 \times (5x + 8)$

$:\implies\sf 24x + 48 = 25x + 40$

$:\implies\sf 48 - 40 = 25x - 24x$

$: \implies \underline{ \boxed{\textsf{\textbf{x = 8 years}}}}$

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☯ $\underline{\boldsymbol{Present\: Age\:of\: Anu\:\&\:Raj:}}$

$\bullet\:\:\textsf{Anu = 4x = 4(8) = \textbf{32 years}}$

$\bullet\:\:\textsf{Raj = 5x = 5(8) = \textbf{40 years}}$