Question

the age of aariv and diya are in the ratio 5:7 after four years from now ratio of their age will 3:4 find their present age​

Answer 1

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The ages of Aariv and Diya are in the ratio $5:7.$ After four years from now, ratio of their age will $3:4.$ Find their present age.

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• The ages of Aariv and Diya are in the ratio $5:7.$

• After four years from now, ratio of their age will $3:4.$

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Their present ages.

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Let their present ages are $5x$ yrs and $7x$ yrs respectively.

After $4$ yrs, there ages will be $(5x+4)$ yrs and $(7x+4)$ yrs respectively.

After four years from now, ratio of their age will $3:4.$

According to condition,

$(5x+4):(7x+4) = 3:4$

We can write the ratios as fractions.

$➳\:{\frac{(5x+4)}{(7x+4)}} = {\frac{3}{4}}$

$➳\:4(5x+4) = 3(7x+4)$

$➳\:20x+16 = 21x+12$

$➳\:20x-21x = 12-16$

$➳\:({\red{-}}x) = ({\red{-}}4)$

Since both sides are negative, $“{\bold{\red{-}}}”$ cancels out.

$➳\:x = 4$

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$x = 4$

By substituting $x$ with $4.$

Aariv's age = $5x = (5×4)=20$

Diya's age = $7x = (7×4)=28$

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Aariv's present age is $20$ yrs and Diya's present age is $28$ yrs.

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