Question

Four years ago the ratio of ages of Chirag and Vanya was 2:3.
Four years hence the ratio of ages of Chirag and Vanya will be 5:7

Find their Present Ages.​

Answer 1

▪Given :-

☆》Four years ago the ratio of ages of Chirag and Vanya was 2:3..

☆》Four years hence the ratio of ages of Chirag and Vanya will be 5:7.

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▪To Find :-

Present ages of Chirag and Vanya.

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▪Solution :-

Let ,

Present age of Chirag = x years

Present age of Vanya = y years

Four years ago ,

Age of Chirag = (x - 4) years

Age of Vanya = (y - 4) years

According to the Given Condition

$\dfrac{x - 4}{y - 4} = \dfrac{2}{3} \\ \\ 3(x - 4) = 2(y - 4) \\ \\ 3x - 12 = 2y - 8\\ \\ \bf \implies3x - 2y = 4 \: \: \: \: .\:. \: .\: \{i \}$

Four years Hence ,

Age of Chirag = (x + 4) years

Age of Vanya = (y + 4) years

According to the Given Condition ,

$\dfrac{x + 4}{y + 4} = \dfrac{5}{7} \\ \\ 7(x + 4) = 5(y + 4) \\ \\ 7x + 28 = 5y + 20 \\ \\ \bf \implies7x - 5y = - 8 \: \: \: \: . \: .\: .\: \{ii \}$

Solving Both Equations ,

We Get ,

$\Large \purple{ \implies  \underline {\boxed{{\bf  {x = 36 \: years}} }}}$

And ,

$\Large \purple{ \implies  \underline {\boxed{{\bf  y = 52 \: years} }}}$

So ,

Present age of Chirag = 36 years

And

Present age of Vanya = 52 years.

$\Large \red{\mathfrak{  \text{W}hich \:   \: are  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswers.}}$

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Answer 2

Given :-

Four years ago the ratio of ages of Chirag and Vanya was 2:3.

Four years hence the ratio of ages of Chirag and Vanya will be 5:7

To Find :-

Present ages

Solution :-

Let the age of Chirag be C and Vanya be V

Four years ago

Age of Chirag = C - 4

Age of Vanya = V - 4

C - 4/V - 4 = 2/3

2(V - 4) = 3(C - 4)

2V - 8 = 3C - 12

2V - 3C = 12 - 8

2V - 3C = 4(1)

After 4 years

Age of Chirag = C + 4

Age of Vanya = V + 4

C + 4/V + 4 = 5/7

5(V + 4) = 7(C + 4)

5V + 20 = 7C + 28

5V - 7C = 20 - 28

5V - 7C = -8 (2)

On Solving we get

V = 40 years

And

C = 56 years