The ratio of the ages of man and his wife is 4:3. After 4 years, the ration will be 9:7. If at the time of marriage, the ratio was 5:3, how many years ago were they married?
The ratio of the ages of man and his wife is 4:3. After 4 years, the ration will be 9:7. If at the time of marriage, the ratio was 5:3, how many years ago were they married?
1). 12
2). 24
3). 5
4). 8
2 answers
Solution :
Let us take the man's age as 'x' and his wife's age as 'y' .
Given;
Ratio of their present age is 4:3 . So,
x/y = 4/3 -------> 1
Ratio of their age after 4 years is 9:7. So,
(x + 4)/ (y + 4 ) = 9/7
By cross multiplication we get
7(x + 4) = 9(y + 4 )
7x + 28 = 9y + 36
7x - 9y = 36 - 28
7x - 9y = 8
From equation 1 we get x = 4y/3,applying it in here we get
7 (4y/3) - 9y = 8
28y/3 - 9y = 8
(28y - 27y)/3 = 8
(y) = 8 ×3
y = 24
Applying the value of y in x = 4y/3 we get,
x = (4 × 24)/ 3
x = 96/3
x = 32
Let us take the no.of years ago which they were married as 'a'
Given:
(x - a )/(y - a) = 5/3
3 (x - a ) = 5 (y - a)
3x - 3a = 5y - 5a
Substituting the value of x and y we get
3 ×32 - 3a = 5 × 24 - 5a
96 - 3a = 120 - 5a
5a - 3a = 120 - 96
2 a = 24
a = 24/2
a = 12
Therefore the man and his wife were married 12 years ago.
The correct option is 1).12
