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
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
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
RELATED QUESTIONS:-
https://brainly.in/question/44382154
https://brainly.in/question/44383146
https://brainly.in/question/43419193
https://brainly.in/question/43604388
https://brainly.in/question/43575188
https://brainly.in/question/44780097