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 \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`

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

`\\ \\`

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

`\\ \\`

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

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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

~
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