Math, asked by NewtonBaba420, 1 month ago

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.​

Answers

Answered by AestheticSoul
4

Required Answer :

  • Present age of Chirag = 36 years
  • Present age of Vanya = 52 years

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 :

  • The present age of Chirag and Vanya

Solution :

Let,

  • Present age of Chirag = x years
  • Present age of Vanya = y years

Their ages ago 4 years :-

Age of Chirag = x - 4 years

Age of Vanya = y - 4 years

According to the question,

⇒ (x - 4)/(y - 4) = 2/3

⇒ 3(x - 4) = 2(y - 4)

⇒ 3x - 12 = 2y - 8

⇒ 3x - 2y = - 8 + 12

⇒ 3x - 2y = 4 ------(1)

Their ages after 4 years :-

Age of Chirag = x + 4 years

Age of Vanya = y + 4 years

According to the question,

⇒ (x + 4)/(y + 4) = 5/7

⇒ 7(x + 4) = 5(y + 4)

⇒ 7x + 28 = 5y + 20

⇒ 7x - 5y = 20 - 28

⇒ 7x - 5y = - 8 -------(2)

Making one of the coefficient same of the equation (1) and (2) :-

= (3x - 2y = 4) × 5

= 15x - 10y = 20 ---------(3)

= (7x - 5y = - 8) × 2

= 14x - 10y = - 16 ------(4)

Solving (3) and (4) :-

15x - 10y = 20

14x - 10y = - 16

-⠀⠀+⠀⠀⠀⠀+⠀

_____________

x⠀⠀⠀⠀⠀= 36

_____________

The value of x = 36

Substitute the value of x in equation (1) :-

= 3x - 2y = 4

= 3(36) - 2y = 4

= 108 - 2y = 4

= - 2y = 4 - 108

= - 2y = - 104

= 2y = 104

= y = 104/2

= y = 52

The value of y = 52

Therefore,

  • Present age of Chirag = x = 36 years
  • Present age of Vanya = y = 52 years
Answered by devanshu1234321
1

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.​

EXPLANATION:-

Let the present age of chirag=x years

And that of vanya=y years

Their age 4 years ago:-

Chirag=x-4

Vanya=y-4

Ratio=2:3

(x-4)/(y-4)=2/3

3x-12=2y-8

3x-2y=4------eq-1

Their age 4 years after:-

Chirag=x+4

Vanya=y+4

Ratio=5:7

(x+4)/(y+4)=5/7

7x+28=5y+29

7x-5y=-8-------eq-2

Multiply eq-1 by 5  and eq-2 by 2

(3x-2y=4)×5

5x-10y=20-----eq-3

(7x - 5y = - 8) × 2

 14x - 10y = - 16 ------eq-4

eq-3-eq-4

15x - 10y = 20

14x - 10y = - 16

-⠀⠀+⠀⠀⠀⠀+⠀

_____________

x⠀⠀⠀       =36  

_____________

So the value of x is 36 :-

Means chrag age is 26 years

Solving the solve of y we will get that value of y is 52

SO vanya age is 52 years

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