Question

The age of hari and harry are in the ratio 8:10 . Eight year from now the ratio of their age will be 10:12 . Find their present ages

a)32,40

b) 30,40

c) 35,40

d)40,30



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Answer 1

GIVEN :–

• The age of hari and harry are in the ratio 8:10.

• Eight year from now the ratio of their age will be 10:12.

TO FIND :–

• Their present age = ?

SOLUTION :–

• Let the age of hari is 'x' .

• And the age of harry is 'y' .

• According to the first condition –

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$\bf \implies \dfrac{x}{y} = \dfrac{8}{10}$

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$\bf \implies x = \dfrac{8}{10}y \: \: \: \: \: - - - eq.(1)$

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• According to the second condition –

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$\bf \implies \dfrac{x+8}{y+8} = \dfrac{8}{10}$

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$\bf \implies \dfrac{x+8}{y+8} = \dfrac{10}{12}$

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$\bf \implies 12(x + 8) = 10(y + 8)$

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$\bf \implies 12x +96 = 10y + 80$

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$\bf \implies 12x = 10y - 16$

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• Using eq.(1) –

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$\bf \implies 12 \left(\dfrac{8y}{10} \right)= 10y - 16$

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$\bf \implies \dfrac{96y}{10} - 10y= - 16$

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$\bf \implies \dfrac{96y - 100y}{10} = - 16$

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$\bf \implies \dfrac{ - 4y}{10} = - 16$

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$\large\implies { \boxed{ \bf y = 40}}$

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• Again Using eq.(1) –

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$\bf \implies x = \dfrac{8}{10}(40)$

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$\large\implies { \boxed{ \bf x=32}}$

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▪︎ The Age of hari is 32 year and age of harry is 40 year.

▪︎ Hence , Option (a) is correct .

Answer 2

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

• The age of Hari and Harry are in the ratio : 8 : 10

• Eight year from now the ratio of their age will be 10:12

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

• The present ages of Hari and Harry

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

Let the common ratio of their ages be x

The age of Hari = 8x

The age of Harry = 10x

After eight years:-

Age of Hari = 8x + 8

Age of Harry = 10x + 8

Given, the ratio after eight years will be 10:12

Therefore:-

$\sf \rightarrow (8x + 8): \: (10x + 8) = 10 \: : \: 12$

$\sf \rightarrow \dfrac{8x + 8}{10x + 8} = \dfrac{10}{12}$

By cross multiplication:-

$\sf \rightarrow {12(8x + 8)} = {10(10x + 8)}$

$\sf \rightarrow {96x + 96} = {100x + 80}$

$\sf \rightarrow {100x - 96x } = {96 - 80}$

$\sf \rightarrow {4x } = {16}$

$\sf \rightarrow {x } = \dfrac{16}{4}$

$\sf \rightarrow {x } = 4$

Therefore:-

Age of Hari = 8x = 8×4 = 32

Age of Harry = 10x = 10×4 = 40

Hence;

$\large\boxed{\sf \pink{ Present \: age \: of \: Hari= 32 \: years} }$

$\large \boxed{\sf \purple{ present \: age \: of \: harry= 40\: years} }$

$\large\bf{ \underline{Option \: (a) \: is \: correct} }$