Math, asked by Anonymous, 1 year ago

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Five years ago, Kabir's mother was 5 times as old as Kabir. If his mother is now three times as as old as Kabir, find their present ages.

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Answers

Answered by Sauron
370

\mathfrak{\large{\underline{\underline{Answer :-}}}}

Kabir is presently 10 years old and his mother is 30 years old.

\mathfrak{\large{\underline{\underline{Explanation :-}}}}

Given :

Five years ago, Kabir's mom was 5 times as old as he was.

Presently, his mom is now three times as as old as Kabir is.

To Find :

Their present Ages

Solution :

\textbf{\small{\underline{Consider the Present Ages -}}}

  • Kabir as x
  • Mother is 3x

\textbf{\small{\underline{Ages before 5 years -}}}

  • Kabir will be (x - 5)
  • Mother will be (3x - 5)

\textbf{\small{\underline{According to the Question -}}}

Kabir's mother was 5 times as old as Kabir was 5 years ago.

\boxed{\sf{5(x-5)=3x-5}}

\tt{\longrightarrow} \:5(x-5)=3x-5

\tt{\longrightarrow} \:5x-25=3x-5

\tt{\longrightarrow} \:5x - 3x=-5 + 25

\tt{\longrightarrow} \:2x=20

\tt{\longrightarrow} \:x =  \dfrac{20}{2}

\tt{\longrightarrow} \:x = 10

Kabir's present age = 10 years

\rule{300}{1.5}

Value of 3x

\tt{\longrightarrow} \:3 \times 10

\tt{\longrightarrow} \:30

Kabir's mother is 30 years old.

\therefore Kabir is presently 10 years old and his mother is 30 years old.

\rule{300}{1.5}

\mathfrak{\large{\underline{\underline{Verification :- }}}}

Place the value of x and check if both the sides (LHS and RHS) are equal or not.

\tt{\longrightarrow} \:5(10-5)=3(10)-5

\tt{\longrightarrow} \:50-25=30-5

\tt{\longrightarrow} \:25=25

\tt{\longrightarrow} \:LHS  =  RHS

\therefore Kabir is presently 10 years old and his mother is 30 years old.


Anonymous: Great answer !
Sauron: Thankies ♥️
Answered by Anonymous
297

Solution :-

As we are provided with :-

Five years ago Kabir's Mother was 5 times old as Kabir.

And Now his Mother is three times as old as Kabir .

Now let us suppose the current age of Kabir be = x .

Then According to the first statement :-

→ 5(x - 5) = Mother age 5 years ago.

And according to the second statement :-

Mother's age = 3x

Now by both statements :-

→ 5(x - 5) + 5 = 3(x)

As Mother's age was 5(x - 5) five years ago then current age = 5(x - 5) + 5

Now we will solve this linear equation :-

→ 5(x - 5) + 5 = 3x

→ 5x - 25 + 5 = 3x

→ 5x - 20 = 3x

→ 5x - 3x = 20

→ 2x = 20

→ x = 10

So we got the current age of Kabir

= x

= 10 years.

Now as the current age of his mother is

= 3x

= 3(10)

= 30

Now verification of the answer :-

Mother's age 5 years ago was 5 times the Kabir's age

→ 30 - 5 = 5(10 - 5)

→ 25 = 5(5)

→ 25 = 25

Therefore As LHS = RHS

Hence the Current ages of

Kabir = 10 years

His Mother = 30 years


Rythm14: Awesome!
Anonymous: Thanks ☺️
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