Question

Arpirta's present age is d years while annaya's is (d-6) years in ten years annay's age will be two thirds of arprita's find annay's present age ?​

Answer 1

Given : Arpita's present age is d years while Annaya's is (d - 6) years & ln ten years Annay's age will be two thirds of Arpirta's.

To Find : Present age of Annaya's ?

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Given that,

• Arpita's present age is d years, while

• Annaya's is (d - 6) years

• AFTER 10 YEARS their ages :

• Arpita's age will be (d + 10) years & Annaya's is (d - 6) years

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$\underline{\frak{According ~to ~the ~Given ~Question~:}}$

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• In ten years Annaya's age will be two thirds of Arpirta's.

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$~~~~~~~~~~{\sf:\implies{Annaya's~age_{(After~10~years)}~=~\dfrac{2}{3}\bigg(Arpita's~age_{(After 10 years)}\bigg)}}$

$~~~~~~~~~~{\sf:\implies{(d~-~6~+~10)~=~\dfrac{2}{3}\bigg(2~+~10\bigg)}}$

$~~~~~~~~~~{\sf:\implies{3(d~-~6~+~10)~=~2(d~+~10)}}$

$~~~~~~~~~~:\implies{\sf{3d~-~18~+~30~=~2d~+~10}}$

$~~~~~~~~~~:\implies{\sf{3d~+~30~=~2d~+~20~+~18}}$

$~~~~~~~~~~:\implies{\sf{3d~+~30~=~2d~+~38}}$

$~~~~~~~~~~:\implies{\sf{3d~=~2d~+~38~-~30}}$

$~~~~~~~~~~:\implies{\sf{3d~=~2d~+~8}}$

$~~~~~~~~~~:\implies{\sf{3d~-~2d~=~8}}$

$~~~~~~~~~~:\implies{\sf{d~=~8}}$

$~~~~~~~~~~:\implies{\underline{\boxed{\frak{\pink{d~=~8~years}}}}}$★

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• Here d donates Present age of Arpita which is 8 years & Present age of Annaya will be (d - 6) = (8 - 6) = 2 years.

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Hence,

$\therefore\underline{\sf{Present ~age~ of ~Annaya~ is~\bf{2~years}}}$