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Please answer this question​

Please answer this question​-example-1

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Part one :

As it is given :

Present age of mom : Present age of son = 6 : 1

Therefore let :

  • Mother's age be 6x

  • Son's age be x

Part two :

Ages after 10 year :

  • Mom's age = 6x + 10

  • Son's age = x + 10

Part three :

The ages after 10 years are given in rational of 8 : 3.

Which means :

Mom's age after 10 years : Son's age after 10 years = 8 :3.

Now :


\scriptsize \purple{ \boxed{ \scriptsize \frac{ \text{Mom's age after 10 years}}{ \text{son's age after 10 years}}= (8)/(3) }} \star


\\ \\

So :


\small\sf \dashrightarrow (6x + 10)/(x + 10) = \sf (8)/(3)


\\ \\


\small\sf \dashrightarrow (3(6x + 10))/(x + 10) = \sf (8)/(1)


\\ \\


\small \sf \dashrightarrow (18x +30)/(x + 10) = \sf (8)/(1)


\\ \\


\small\sf \dashrightarrow (18x +30)/(1) = \sf (8(x + 10))/(1)


\\ \\


\small \sf \dashrightarrow 18x +30= \sf 8(x + 10)


\\ \\


\small\sf \dashrightarrow 18x +30= \sf 8x + 80


\\ \\


\small\sf \dashrightarrow 18x - 8x +30= \sf 80


\\ \\


\small \sf \dashrightarrow 10x +30= \sf 80


\\ \\


\small \sf \dashrightarrow 10x = \sf 80 - 30


\\ \\


\small \sf \dashrightarrow 10x = \sf 50


\\ \\


\small \sf \dashrightarrow (10x)/(10) = \sf (50)/(10)


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\small \sf \dashrightarrow (1\cancel0x)/(1\cancel0) = \sf (5\cancel0)/(1\cancel0)


\\ \\


\small\bf \dashrightarrow x = \pink 5


\\

Part four :

We know :


\footnotesize \hookrightarrow \sf Son's \: age = x


\footnotesize \hookrightarrow \sf Son's \: age = \red{5 \: years}


\\ \\


\footnotesize \hookrightarrow \sf Mother's \: age = 6x


\footnotesize\hookrightarrow \sf Mother's \: age = 6 * 5


\footnotesize \hookrightarrow \sf Mother's \: age = \bf \red{30 \: years}

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And all we are done ! ㋛

~
\pmb{\cal W\frak{indy}M\frak{int}}

User Lonesomeday
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