Question

The ratio of the percentage of viju to that of aju is 7:2 four years from now, the ratio of the ages of viju to aju will be 5:2 what was viju's age 6years ago ?ya 5:2 what was

Answer 1

$\large \bf \clubs \:  Appropriate \: Question :-$

The ratio of the Present Ages of Viju to that of Aju is 7 : 2.Four years from now, the ratio of the Ages of viju to aju will be 5 : 2. What was viju's age 6 years ago ?

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$\large \clubs \: \bf Given : -$

• The ratio of the Present Ages of Viju to that of Aju is 7 : 2.

• Four years from now, the ratio of the Ages of viju to aju will be 5 : 2.

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$\large \clubs \: \bf To \: Find : -$

• Viju's Age 6 years Ago

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$\large \clubs \: \bf Solution : -$

Let,

Present Age of Viju = 7x years

Present Age of Aju = 2x years

《After 4 Years》

• Age of Viju = (7x + 4) years

• Age of Aju = (2x + 4) years

✏ According To Question :

$\dfrac{7 \text x + 4}{2\text x + 4} = \dfrac{5}{2}$

$:\longmapsto2(7\text x + 4) = 5(2\text x + 4)$

$:\longmapsto14\text{x + 8 = 10x + 20}$

$:\longmapsto14\text x - 10\text x = 20 - 8$

$:\longmapsto4\text x = 12$

$:\longmapsto\text x = \cancel\dfrac{12}{4}$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 3} }}}$

So,

• Present Age of Viju = 7 × 3 = 21 years

《 6 Years Ago 》

Viju's Age = 21 - 6

☆ Hence,

$\large\underline{\pink{\underline{\frak{\pmb{\text Viju's \: \text Age =15 \: \text years }}}}}$

$\\ \Large\red{\mathfrak{  \text{W}hich \:\:is\:\: the\:\: required} }\\ \LARGE \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

$\overline{\underline{\boxed{\sf GIVEN \darr}}}$

The ratio of the Present Ages of Viju to that of Aju is 7 : 2.Four years from now, the ratio of the Ages of Viju to Aju will be 5 : 2. What was Viju's age 6 years ago ?

$\overline{\underline{\boxed{\sf SOLUTION \darr}}}$

Given that :

Present Age Ratio :

• Viju = 7

• Aju = 2

After 4 years :

Ratio of Viju's age = 5

Ratio of Aju's age = 2

Let the constant multiple be x

Therefore, Present ages :

Viju's present age is 7x

Aju's present age is 2x

After 4 years

It means 4 will be added to both the ages of Viju and Aju

Viju's age after 4 years = 7x + 4

Aju's age after 4 years = 2x + 4

Ratio of Ages after 4 years

Viju = 5

Aju = 2

Hence, the equation is :

$\looparrowright \sf{ \red{ \frac{7x + 4}{2x + 4} = \frac{5}{2} }}$

By cross multiplying we get

$\looparrowright\sf \green{2(7x + 4) = 5(2x + 4)}$

Simplifying it we get

$\looparrowright \sf \blue{14x + 8 = 10x + 20}$

Transposing them on the other side

$\sf \looparrowright \purple{14x - 10x =20 - 8 }$

$\looparrowright \sf \pink{4x = 12}$

Again, cross multiplying the equation to get the simplest result

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \overline{ \underline{ \boxed{ \sf \color{navy}{x = 3}}}}$

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Now, their present ages are :

Viju's present age = 7x = 7 × 3 = 21 years

Aju's present age = 4x = 4 × 3 = 12 years

Now, it is told to find the age of Viju 6 years ago

So, Viju's age before six years

⟼ Present age - 6 years

⟼ 21 years - 6 years

⟼ 15 years

Therefore, his age was 15 years