Question

Age of Remya and double of Sofi added together gives 28. Three-fourth of Remya's age added to one-fourth of Sofi's age gives 11. find the age of Remya and the age of sofi​

Answer 1

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

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

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• Age of Remya and double of Sofi added together gives 28

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• Three-fourth of Remya's age added to one-fourth of Sofi's age gives 11

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

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• The age of Remya and the age of sofi

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

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• Let the present age of Remya be "R"

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• Let the present age of Sofi be "S"

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

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$\underline{\bold{\texttt{Double the age of Sofi :}}}$

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➜ 2 × S

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➠ 2S

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Age of Remya and double of Sofi added together gives 28

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➜ R + 2S = 28 ------ (1)

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$\underline{\bold{\texttt{Three fourth of Remya's age :}}}$

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➜ $\sf R \times \dfrac { 3 } { 4 }$

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➠ $\sf \dfrac { 3R } { 4 }$

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$\underline{\bold{\texttt{One fourth of Sofi's age :}}}$

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➜ $\sf S\times \dfrac { 1} { 4 }$

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➠ $\sf \dfrac { S} { 4 }$

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Also given that ,three-fourth of Remya's age added to one-fourth of Sofi's age gives 11

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So,

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➜ $\sf \dfrac { 3R } { 4 } + \dfrac { S } { 4 } = 11$

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➜ 3R + S = 11 × 4

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➜ 3R + S = 44 ------ (2)

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⟮ Multiplying equation (2) with 2 ⟯

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➜ 2(3R + S) = 2(44)

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➜ 6R + 2S = 88 -------- (3)

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⟮ Subtracting equation (1) from (3) ⟯

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➜ 6R + 2S - (R + 2S) = 88 - 28

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➜ 6R + 2S - R - 2S = 60

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➜ 5R = 60

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➜ $\sf R = \dfrac { 60 } { 5 }$

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➨ R = 12 ------ (4)

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• Hence age of Remya is 12 years

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⟮ Putting R = 12 from (4) to (1) ⟯

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➜ R + 2S = 28

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➜ 12 + 2S = 28

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➜ 2S = 28 - 12

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➜ 2S = 16

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➜ $\sf S = \dfrac { 16 } { 2 }$

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➨ S = 8

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• Hence age of Sofi is 8 years

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∴ The ages of Remya and Sofi are 12 & 8 years respectively

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Answer 2

Answer:

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

Answer:

\:\:

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

Given:−

\:\:

Age of Remya and double of Sofi added together gives 28

\:\:

Three-fourth of Remya's age added to one-fourth of Sofi's age gives 11

\:\:

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

ToFind:−

\:\:

The age of Remya and the age of sofi

\:\:

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

Solution:−

\:\:

Let the present age of Remya be "R"

\:\:

Let the present age of Sofi be "S"

\:\:

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

Accordingtothe question:

\:\:

\underline{\bold{\texttt{Double the age of Sofi :}}}

Double the age of Sofi :

\:\:

➜ 2 × S

\:\:

➠ 2S

\:\:

Age of Remya and double of Sofi added together gives 28

\:\:

➜ R + 2S = 28 ------ (1)

\:\:

\underline{\bold{\texttt{Three fourth of Remya's age :}}}

Three fourth of Remya’s age :

\:\:

➜ \sf R \times \dfrac { 3 } { 4 }R×

4

3

\:\:

➠ \sf \dfrac { 3R } { 4 }

4

3R

\:\:

\underline{\bold{\texttt{One fourth of Sofi's age :}}}

One fourth of Sofi’s age :

\:\:

➜ \sf S\times \dfrac { 1} { 4 }S×

4

1

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➠ \sf \dfrac { S} { 4 }

4

S

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Also given that ,three-fourth of Remya's age added to one-fourth of Sofi's age gives 11

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So,

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➜ \sf \dfrac { 3R } { 4 } + \dfrac { S } { 4 } = 11

4

3R

+

4

S

=11

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➜ 3R + S = 11 × 4

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➜ 3R + S = 44 ------ (2)

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⟮ Multiplying equation (2) with 2 ⟯

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➜ 2(3R + S) = 2(44)

\:\:

➜ 6R + 2S = 88 -------- (3)

\:\:

⟮ Subtracting equation (1) from (3) ⟯

\:\:

➜ 6R + 2S - (R + 2S) = 88 - 28

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➜ 6R + 2S - R - 2S = 60

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➜ 5R = 60

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➜ \sf R = \dfrac { 60 } { 5 }R=

5

60

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➨ R = 12 ------ (4)

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Hence age of Remya is 12 years

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⟮ Putting R = 12 from (4) to (1) ⟯

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➜ R + 2S = 28

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➜ 12 + 2S = 28

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➜ 2S = 28 - 12

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➜ 2S = 16

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➜ \sf S = \dfrac { 16 } { 2 }S=

2

16

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➨ S = 8

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Hence age of Sofi is 8 years

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∴ The ages of Remya and Sofi are 12 & 8 years respectively

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