Question

Rita age now is thrice the age of Latha. eight years ago rita age was 4 times the age of Latha . find their present ages.​

Answer 1

Given: Rita's age now is thrice the age of Latha. Eight years ago, Rita age was four times the age of Latha.

Need to find: Their present ages?

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❍ Let's Consider, the present age of Latha be x years. Then, Rita's age would be 3x years. i.e Rita age now is thrice the age of Latha.

⠀

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

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• Eight years ago, the Rita age was four times the age of Latha.

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⌑ Eight years ago, their ages —

• Latha's age = (x – 8) years
• Rita's age = (3x – 8) years

⠀

$:\implies\sf Rita's \; age = 4\Big\{Latha's\;age\Big\}$

$:\implies\sf \Big\{3x - 8\Big\}= 4\Big\{x - 8\Big\}$

$:\implies\sf 3x - 8 = 4x - 32$

$:\implies\sf 3x - 4x = -32 + 8$

$:\implies\sf \cancel{-}\;x= \cancel{-}\; 24$

$:\implies\underline{\boxed{\pmb{\frak{x = 24}}}}\;\bigstar$

Therefore,

• Present age of Latha, x = 24 years
• Present age of Rita, 3x = 3(24) = 72 years

⠀

$\therefore{\underline{\textsf{Hence, present age of Latha and Rita is \textbf{24 years, 72 years} respectively.}}}$

Answer 2

Answer:

Given :-

• Rita age now thrice the age of Latha.
• Eight years ago Rita age was 4 times the age of Latha.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf{Present\: Age\: of\: Latha =\: y\: years}$

$\mapsto \bf{Present\: Age\: of\: Rita =\: 3y\: years}$

◘ 8 years ago :

$\leadsto \sf Age\: of\: Latha =\: (y - 8)\: years$

$\leadsto \sf Age\: of\: Rita =\: (3y - 8)\: years$

According to the question,

$\bigstar$ 8 years ago Rita age was 4 times the age of Latha.

$\implies \sf 3y - 8 =\: 4(y - 8)$

$\implies \sf 3y - 8 =\: 4y - 32$

$\implies \sf 3y - 4y =\: - 32 + 8$

$\implies \sf {\cancel{-}} y =\: {\cancel{-}} 24$

$\implies \sf\bold{\purple{y =\: 24}}$

➲ Hence, the required ages of Latha and Rita are :

❒ Present Age Of Latha :

$\longrightarrow \sf Present\: Age_{(Latha)} =\: y\: years$

$\longrightarrow \sf\bold{\red{Present\: Age =\: 24\: years}}$

❒ Present Age Of Rita :

$\longrightarrow \sf Present\: Age_{(Rita)} =\: 3y\: years$

$\longrightarrow \sf Present\: Age_{(Rita)} =\: 3(24)\: years$

$\longrightarrow \sf Present\: Age_{(Rita)} =\: 3 \times 24\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Rita)} =\: 72\: years}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: Latha\: and\: Rita\: are\: 24\: years\: and\: 72\: years\: respectively\: .}}}}$

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VERIFICATION :-

$\leadsto \sf 3y - 8 =\: 4(y - 8)$

By putting y = 24 we get

$\implies \sf 3(24) - 8 =\: 4(24 - 8)$

$\implies \sf 72 - 8 =\: 4(16)$

$\implies \sf\bold{\pink{64 =\: 64}}$

Hence, Verified.