Question

3 years ago anita's age was four times the age of smita at that time five years hence anita's age will be twice the age of smita then find their present ages​

Answer 1

AnSwer :

Let the age of Anita be m years and age of Smita be n years respectively.

⌑ Three years ago, their ages —

• Anita's age = (m – 3)
• Smita's age = (n – 3)

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• As Per Question, we've:

• Three years ago Anita's age was four times the age of Smita at that time.

☆ 4(Smita's age) = Anita's age

➟ 4(n – 3) = (m – 3)

➟ 4n – 12 = m – 3

➟ m = 4n – 9 ⠀⠀⠀⠀⠀⠀⠀⠀⠀—eq. ( I )

⠀⠀

• Five years Hence, Anita's age will be twice the age of Smita.

⌑ After five years, their ages —

• Anita's age = (m + 5)
• Smita's age = (n + 5)

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⠀⠀

☆ Anita's age = 2(Smita's age)

➟ (m + 5) = 2(n + 5)

➟ m + 5 = 2n + 10

➟ m = 2n + 10 – 5

➟ m = 2n + 5 ⠀⠀⠀⠀⠀⠀⠀⠀⠀—eq. ( II )

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» From eqₙ ( I ) & eqₙ ( II ) :

⇥ 4n – 9 = 2n + 5

⇥ 4n – 2n = 9 + 5

⇥ 2n = 14

⇥ n = 14⁄2

⇥ n = 7

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✇ Putting value of n in eqₙ ( II ) :

⇥ m = 2n + 5

⇥ m = 2(7) + 5

⇥ m = 14 + 5

⇥ m = 19

⠀

∴ Hence, the present age of Anita and Samita are 7 and 19 years respectively. $\;$

Answer 2

Answer:

Given :-

• 3 years ago Anita's age was four times, the age of Smita at that time, five years hence Anita's age will be twice the age of Smita.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(Anita)} =\: a\: years$

$\mapsto \bf Present\: Age_{(Smita)} =\: b\: years$

$\clubsuit\: \: \sf\boxed{\bold{\green{In\: the\: 1^{st}\: case\: :-}}}$

❒ 3 years ago their ages will be :

$\leadsto \sf Age\: of\: Anita =\: (a - 3)\: years$

$\leadsto \sf Age\: of\: Smita =\: (b - 3)\: years$

Now, according to the question,

$\bigstar$ 3 years ago, Anita's age was four times, the age of Smita at that time.

$\implies \sf 4(b - 3) =\: a - 3$

$\implies \sf 4(b) - 4(3) =\: a - 3$

$\implies \sf 4b - 12 =\: a - 3$

$\implies \sf 4b - a =\: - 3 + 12$

$\implies \sf 4b - a =\: 9$

$\implies \sf 4b - 9 =\: a$

$\implies \sf\bold{\purple{a =\: 4b - 9\: ------\: (Equation\: No\: 1)}}$

$\clubsuit\: \: \sf\boxed{\bold{\green{In\: the\: 2^{nd}\: case\: :-}}}$

$\bigstar$ Five years hence, Anita's age will be twice the age of Smita.

❒ 5 years hence their ages will be :

$\leadsto \sf Age\: of\: Anita =\: (a + 5)\: years$

$\leadsto \sf Age\: of\: Smita =\: (b + 5)\: years$

According to the question,

$\implies \sf a + 5 =\: 2(b + 5)$

$\implies \sf a + 5 =\: 2(b) + 2(5)$

$\implies \sf a + 5 =\: 2b + 10$

$\implies \sf a - 2b =\: 10 - 5$

$\implies \sf a - 2b =\: 5$

$\implies \sf\bold{\purple{a =\: 5 + 2b\: ------\: (Equation\: No\: 2)}}$

Now, from the equation no 1 and equation no 2 we get,

$\implies \sf 4b - 9 =\: 5 + 2b$

$\implies \sf 4b - 2b =\: 5 + 9$

$\implies \sf 2b =\: 14$

$\implies \sf b =\: \dfrac{\cancel{14}}{\cancel{2}}$

$\implies \sf b =\: \dfrac{7}{1}$

$\implies \sf\bold{\pink{b =\: 7}}$

Again, by putting the value of b = 7 in the equation no 1 we get,

$\implies \sf a =\: 4b - 9$

$\implies \sf a =\: 4(7) - 9$

$\implies \sf a =\: (4 \times 7) - 9$

$\implies \sf a =\: 28 - 9$

$\implies \sf\bold{\pink{a =\: 19}}$

Hence, their present ages are :

$\longrightarrow \sf\bold{\red{Present\: Age_{(Anita)} =\: 19\: years}}$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Smita)} =\: 7\: years}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: Anita\: and\: Smita\: are\: 19\: years\: and\: 7\: years\: respectively\: .}}}}$