Question

Reema is one seventh as old as her cousin. In 8 years she will be one third as old as her
cousin. Their present ages are:

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{\tt{Given :-}}}$

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• Reema is one seventh as old as her cousin

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• After 8 years Reema will be one third as old as her cousin

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

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• Their present ages

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let the present age of Reema be "r"

• Let the present age of cousin be "c"

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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〚 Reema is one seventh as old as her cousin 〛

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➜ r = $\rm \dfrac { 1 } { 7 } \times c$

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➜ 7r = c ------ (1)

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$\underline{\bold{\texttt{Reema's age after 8 years :}}}$

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➟ r + 8

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$\underline{\bold{\texttt{Cousin's age after 8 years :}}}$

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➟ c + 8

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〚 Also given that , After 8 years Reema will be one third as old as her cousin 〛

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So,

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➜ r + 8 = $\dfrac { 1 } { 3 }\times ( c + 8 )$

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➜ 3r + 24 = c + 8 ------ (2)

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$\underline{\bold{\texttt{Putting c = 7r from (1) to (2) }}}$

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➜ 3r + 24 = 7r + 8

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➜ 7r - 3r = 24 - 8

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➜ 4r = 16

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➜ r = $\rm \dfrac { 16 } { 4 }$

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➨ r = 4 ----- (3)

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• Hence Reema is 4 years old

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$\underline{\bold{\texttt{Putting r = 4 from (3) to (1) }}}$

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➜ 7r = c

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➜ 7 × 4 = c

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➨ c = 28

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• Hence her cousin is 28 years old

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So, Reema ad her cousin are 4 & 28 years old respectively .

Answer 2

Given :

• Reema = 1 / 7 as old as her cousin

• In 8 years = 1 / 3 as old as her cousin

To find :

• Their present ages

According to the question :

Let the age of Cousin be ' x ' and Reema be ' y '

Reema will be 7 years older than her cousin

• ∴ x = 1 / 7 y

• y = 7x .....[ 1 st equation ]

After 8 years,

• Cousin will be = x + 8

• Reema will be = y + 8

Equation :

↦( After 8 years age of Cousin ) = 1 / 3 ( After 8 years age of Reema )

⟹ ( x + 8 ) = 1 / 3 ( y + 8 )

⟹ 3 ( x + 8 ) = ( y + 8 )

⟹ 3 ( x + 8 ) = ( [ 1 st equation ] + 8 )

⟹ 3 ( x + 8 ) = 7x + 8

⟹ 3x + 24 = 7x + 8

⟹ 7x - 3x = 24 - 8

⟹ 4x = 16

⟹ x = 16 / 4

⟹ x = 4

We get :

➳ Cousin = 4 years

➳ 1 st Equation = 7x = 7 × 4 = 28 years

∴ Reema = 28 years and Cousin = 4 years

So, It's Done !!