Question

Shobo's mother's present age is six times Shobo's present age. Shobo's age five years from now will be one third of his mother's present age. What are their present ages?​

Answer 1

Answer:

Question:-

Shobo's mother's present age is six times Shobo's present age. Shobo's age five years from now will be one third of his mother's present age. What are their present ages?

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Given :-

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1. Shobo's mother's present age is 6 times Shobo's present age.

1. Shobo's age 5 years from now will be 1/3 of his mother's present age.

To find :-

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• Their present ages.

Solution :-

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• Consider,

Present age of Shobo's Mother= x years

Present age of Shobo's = y years

According to the 1st condition :-

Shobo's mother's present age is 6 times Shobo's present age.

$\longrightarrow\sf{x=6y \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(1)}$

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According to the 2nd condition :-

Shobo's age 5 years from now will be 1/3 of his mother's present age.

$\longrightarrow\sf{ \big(y + 5 \big)=\dfrac{1}{3}\times\:x}$

$\longrightarrow\sf{y+5=\dfrac{x}{3}}$

$\sf\longrightarrow\sf{y+5=\dfrac{6y}{3} \qquad \therefore\bigg[Put\:x=6y\: from\:eq(1) \bigg]}$

$\longrightarrow\sf{y+5=2y}$

$\longrightarrow\sf{y-2y=-5}$

$\qquad \longrightarrow\boxed{\purple{\sf\sf{y=5}}}$

Present age of Shobo = 5 years

Now , put y = 5 in eq(1) for getting the value of x.

$\longrightarrow\sf{x=6y}$

$\longrightarrow\sf{x=6\times\:5}$

$\qquad\longrightarrow\boxed{\purple{\sf{x=30}}}$

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Present age of Shobo's Mother = 30 years.

Therefore , the present age of Shobo is 5 years & present age of Shobo's Mother is 30 years.

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Answer 2

Let the present age of Shobo be x years .

Then, Shobo's mother's age =6x years

After 5 years: Shobo's age =(x+5) years 

∴(x+5)=$\sf \dfrac{1}{3}$×(6x)

On cross multiplying, we get

⇒3×(x+5)=6x 

⇒3x+15=6x

⇒3x−6x=−15

⇒3x=−15

Taking 3 to RHS

⇒x=$\sf \dfrac{-15}{3}$

$\sf \orange{⇒x=5}$

Given that shobo's Mother present age is 6 times Shobo's present age

∴5×6=$\sf \pink{30 years}$

Therefore, present age of Shobo is 5 years and his mother is 30 years.