Question

Please answer this question​

Answer 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 :

$\scriptsize \purple{ \boxed{ \scriptsize \dfrac{ \text{Mom's age after 10 years}}{ \text{son's age after 10 years}}= \dfrac{8}{3} }} \star$

So :

$\small\sf \dashrightarrow \dfrac{6x + 10}{x + 10} = \sf \dfrac{8}{3}$

$\small\sf \dashrightarrow \dfrac{3(6x + 10)}{x + 10} = \sf \dfrac{8}{1}$

$\small \sf \dashrightarrow \dfrac{18x +30}{x + 10} = \sf \dfrac{8}{1}$

$\small\sf \dashrightarrow \dfrac{18x +30}{1} = \sf \dfrac{8(x + 10)}{1}$

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

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

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

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

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

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

$\small \sf \dashrightarrow \dfrac{10x}{10} = \sf \dfrac{50}{10}$

$\small \sf \dashrightarrow \dfrac{1\cancel0x}{1\cancel0} = \sf \dfrac{5\cancel0}{1\cancel0}$

$\small\bf \dashrightarrow x = \pink 5$

Part four :

We know :

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

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

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

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

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

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And all we are done ! ㋛

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