The ages of Aatif and Aasif are in the ratio of 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.
Answers
Question
The ages of Aatif and Aasif are in the ratio of 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.
Solution
Given :-
- The ages of Aatif and Aasif are in the ratio of 5:7.
- Four years from now the ratio of their ages will be 3:4.
Find :-
- Age of Aatif & Aasif .
Explanation
Let,
- Age of Aatif = x years
- Age of Aasif = y years
A/C to question
(The ages of Aatif and Aasif are in the ratio of 5:7. )
==> x : y = 5 : 7
==> x/y = 5/7
==> 7x - 5y = 0 ---------------Equ(1)
Again,
( Four years from now the ratio of their ages will be 3:4. ).
==> (x + 4) : (y + 4) = 3 :4
==> (x+4)/(y+4) = 3/4
==> 4*(x+4) = 3*(y+4)
==> 4x - 3y = 12 - 16
==> 4x - 3y = -4
Or,
==> 4x - 3y = -4 ------------Equ(2)
Multiply , by 5 in equ(2) & 3 in equ(1)
- 21x - 15y = 0
- 20x - 15y = -20
______________Sub. it's
==> 21x - 20x = 20
==> x = 20
Keep value of x in equ(2)
==> 4 * (20) - 3y = - 4
==> 3y = -4 - 80
==> y = - 84/3
==> y = - 28
But, we know
Age be always positive .
So, (-ve) sign is negligible
Hence
- Age of Aatif (x) = 20 years
- Age of Aasif (y) = 28 years.
__________________
Given
- Ratio of age of Aatif and Aasif = 5 : 7
- Ratio of age of Aatif and Aasif after four years = 3 : 4
To Find
- Present age of Aatif.
- Present age of Aasif
Solution :
Let, the multiple of ratio be x
age of Aatif and Aasif after four years = 3 : 4
⇒ 5x + 4 : 7x + 4 = 3 : 4
⇒ 20x + 16 = 21x + 12
⇒ 16 - 12 = 21x - 20x
⇒ 4 = x
★ Present age of Aatif = 5x
→ Present age of Aatif = 5 × 4
→ Present age of Aatif = 20
★ Present age of Aasif = 7x
⇒ Present age of Aasif = 7 × 4
⇒ Present age of Aasif = 28