Question

Rahul is thrice as old as Sulekha. Four years ago his age was four times Sulekha's age. The present age of Rahul is ___________.

Answer 1

Answer:-

★ First let us define x:

Let Sulekha be x years old.

Rahul will be 3x

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★ Second, find their age 4 years ago:

Four years ago,

Sulekha = x - 4

Rahul = 3x - 4

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★ Third, form equation:

Four years ago, Rahul's age was 4 times Sulekha's age:

3x - 4 = 4(x - 4)

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★ Fourth, solve x:

3x - 4 = 4(x - 4)

3x - 4 = 4x - 16

x = 12

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$\bigstar$ Fifth, find their age:

Sulekha = x = 12 years old

Ruhul = 3x = 3(12) = 36 years old

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Hence, Sulekha is 12 years old and Ruhul is 36 years old.

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Answer 2

Solution :

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

Rahul is thrice as old as Sulekha. Four years ago, his age was four times sulekha' age.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The present age of Rahul's age.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Let the present age of Rahul be r years

Let the present age of Sulekha be m years

A/q

$\mapsto\bf{r=3m...................(1)}$

$\blacksquare\bf\large{\underline{\underline{\bf{4\:years\:AgO\::}}}}}$

The age of Rahul be = (r-4) years.

The age of Sulekha be = (m-4) years.

So;

$\implies\sf{(r-4)=4(m-4)}\\\\\implies\sf{r-4=4m-16}\\\\\implies\sf{3m-4=4m-16\:\:\:\:\:\:[from(1)]}\\\\\implies\sf{3m-4m=-16+4}\\\\\implies\sf{\cancel{-}m=\cancel{-}12}\\\\\implies\sf{\pink{m=12\:years}}$

Putting the value of m in equation (1),we get;

$\implies\sf{r=3(12)}\\\\\implies\sf{\pink{r=36\:years}}$

Thus;

The present age of Rahul is r = 36 years.

The present age of Sulekha is m = 12 years.