Question

4 year ago the ratio of the age of A and B was 2:3 and after 4 year it become 5:7 find their present ages
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Answer 1

Answer:

2x = 16 years old

3x = 24 years old

Step-by-step explanation:

A:B = 2:3

After 4 years,

A:B = 5:7

or, 2x+4/3x+4 = 5/7

or, 7(2x+4) = 5(3x+4)

or, 14x+28 = 15x+20

or, 14x-15x = 20-28

or, -x = -8

or, x = 8

Therefore, present ages of A and B are:

2x = 16 years old

3x = 24 years old

Answer 2

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

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

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• 4 year ago the ratio of the age of A and B was 2:3

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• After 4 year the ratio become 5:7

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

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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 A be "x"

• Let the present age of B be "y"

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$\underline{\bold{\texttt{A's age 4 years ago :}}}$

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➠ x - 4

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$\underline{\bold{\texttt{B's age 4 years ago :}}}$

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➠ y - 4

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

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4 year ago the ratio of the age of A and B was 2:3

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➠ (x - 4):(y - 4) = 2:3

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➜ $\sf \dfrac { x - 4 } { y - 4 } = \dfrac { 2 } { 3 }$

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➜ 3x - 12 = 2y - 8

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➜ 3x - 2y = - 8 + 12

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➜ 3x - 2y = 4 ------- (1)

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$\underline{\bold{\texttt{A's age after 4 years :}}}$

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➠ x + 4

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$\underline{\bold{\texttt{B's age after 4 years :}}}$

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➠ y + 4

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Given that , after 4 year the ratio become 5:7

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➠ (x + 4):(y + 4) = 5:7

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➜ $\sf \dfrac { x + 4 } { y + 4 } = \dfrac { 5 } { 7 }$

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➜ 7x + 28 = 5y + 20

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➜ 7x - 5y = 20 - 28

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➜ 7x - 5y = -8 -------- (2)

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⟮ Multiplying equation (1) by 5 ⟯

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➜ 3x - 2y = 4

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➜ 15x - 10y = 20 ------- (3)

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⟮ Multiplying equation (2) by 2 ⟯

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➜ 7x - 5y = -8

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➜ 14x - 10y = -16 -------- (4)

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⟮ Subtracting equation (4) from (3) ⟯

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➜ 15x - 10y - 14x + 10y = 20 + 16

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➨ x = 36 ------ (5)

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• Hence present age of A is 36 years

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⟮ Putting x = 36 from (5) to (1) ⟯

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➜ 3x - 2y = 4

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➜ 3(36) - 2y = 4

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➜ 108 - 2y = 4

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➜ 2y = 108 - 4

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➜ 2y = 104

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➜ $\sf y = \dfrac { 104 } { 2 }$

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➨ y = 52

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• Hence the present age of B is 52 years

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∴ Present ages of A and B are 36 years & 52 years respectively

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