Question

4 years ago Meera's age is 3 times of manu's age. After 8 years Meera's age is twice of the manu's age. Find the present age of both.

Answer 1

Answer :

Let the present age of Meera be x years and Manu's age be y years respectively.

Their ages four years ago,

• Meera's age = (x – 4) years
• Manu's age = (y – 4) years

⠀

$\underline{\bigstar\:\boldsymbol{According\; to\; the\; Question :}}$

• Four years ago, Meera's age was three times the age of Manu.

$:\implies\sf~~~ (x - 4) = 3(y - 4)$

$:\implies\sf ~~~x- 4 = 3y - 12$

$:\implies\sf ~~~x - 3y = - 8 \qquad\qquad\qquad\sf\Bigg\lgroup eq^{n} \;(i)\Bigg\rgroup$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

Also,

• After eight years Meera's age is twice the age of Manu.

⠀⠀⠀

Their ages after eight years,

• Meera's age = (x + 8) years
• Manu's age = (y + 8) years

$:\implies\sf ~~~(x + 8) = 2(y + 8)$

$:\implies\sf ~~~x + 8 = 2y + 16$

$:\implies\sf ~~~x - 2y = 8\qquad\qquad\qquad\sf\Bigg\lgroup eq^{n} \;(ii)\Bigg\rgroup$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀$\underline{\bf{\dag} \:\:\mathfrak{Using\;eq^{n}\;(i)\;\&\;eq^n \;(ii)\: :}}$⠀⠀⠀⠀

$\longrightarrow\sf ~~~x - 2y - x - 3y = 8 + 8$

$\longrightarrow\sf ~~~-2y + 3y = 16$

$\longrightarrow{\pmb{\sf ~~~ y = 16}}$

⠀⠀⠀$\underline{\bf{\dag} \;\:\mathfrak{Using\;eq^{n}\;(ii)\: :}}$⠀⠀⠀⠀

$\longrightarrow\sf~~~x - 2y = 8$

$\longrightarrow\sf~~~ x - 2(16) = 8$

$\longrightarrow\sf\;\;\; x - 32 = 8$

$\longrightarrow\sf \;\;\;x = 8 + 32$

$\longrightarrow{\pmb{\sf\;\;\; x = 40}}$

$\therefore{\underline{\textsf{Hence, Meera's age and Manu's age is \textbf{16 years, 40 years} respectively.}}}$

Answer 2

Answer:

Given :-

• 4 years ago Meera's age is 3 times of Manu's age.
• After 8 years Meera's age is twice of the Manu's age.

To Find :-

• What is their present ages.

Solution :-

Let,

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

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

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

❒ 4 years ago their ages will be :

$\leadsto \sf Age_{(Meera)} =\: (a - 4)\: years$

$\leadsto \sf Age_{(Manu)} =\: (b - 4)\: years$

According to the question,

$\bigstar$ 4 years ago, Meera's age is 3 times of Manu's age.

$\implies \bf \bigg\{Age_{(Meera)}\bigg\} =\: 3\bigg\{Age_{(Manu)}\bigg\}$

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

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

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

$\implies \sf\bold{\purple{a - 3b =\: - 8\: ------\: (Equation\: No\: 1)}}$

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

❒ After 8 years their ages will be :

$\leadsto \sf Age_{(Meera)} =\: (a + 8)\: years$

$\leadsto \sf Age_{(Manu)} =\: (b + 8)\: years$

According to the question,

$\bigstar$ After 8 years Meera's age is twice of the Manu's age.

$\implies \bf \bigg\{Age_{(Meera)}\bigg\} =\: 2\bigg\{Age_{(Manu)}\bigg\}$

$\implies \sf (a + 8) =\: 2(b + 8)$

$\implies \sf a + 8 =\: 2b + 16$

$\implies \sf a - 2b =\: 16 - 8$

$\implies \sf\bold{\purple{a - 2b =\: 8\: ------\: (Equation\: No\: 2)}}$

By subtracting the equation no 1 from the equation no 2 we get,

$\implies \sf a - 3b - (a - 2b) =\: - 8 - 8$

$\implies \sf a - 3b - a + 2b =\: - 16$

$\implies \sf {\cancel{a}} {\cancel{- a}} + 2b - 3b =\: - 16$

$\implies \sf 2b - 3b =\: - 16$

$\implies \sf {\cancel{-}} b =\: {\cancel{-}} 16$

$\implies \sf\bold{\blue{b =\: 16}}$

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

$\implies \sf a - 3b =\: - 8$

$\implies \sf a - 3(16) =\: - 8$

$\implies \sf a - 48 =\: - 8$

$\implies \sf a =\: - 8 + 48$

$\implies \sf\bold{\blue{a =\: 40}}$

Hence, their required present ages are :

➲ Present Age Of Meera :

$\longrightarrow \sf Present\: Age_{(Meera)} =\: a\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Meera)} =\: 40\: years}}$

➲ Present Age Of Manu :

$\longrightarrow \sf Present\: Age_{(Manu)} =\: b\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Manu)} =\: 16\: years}}$

${\footnotesize{\bold{\underline{\therefore\: The\: present\: age\: of\: Meera\: and\: Manu\: is\: 40\: years\: and\: 16\: years\: respectively\: .}}}}$