The ratio of the ages of husband and wife is 4:3. After 4 years the ratio will 9:7 . At the time of marriage the ratio was 5:3 , then how many years ago they got married?
h/w = 4/3
(h+4)/(w+4) = 9/7
h=32, w=24
(h-m)/(w-m) = 5/3
(32-m)/(24-m) = 5/3
m=12
They were married 12 years ago, when the ratio of their ages was 20/12 = 5/3
She was a child bride!
Thanks alot
Let's assume that the husband's age is 4x and the wife's age is 3x.
According to the given information, after 4 years, the ratio of their ages will be 9:7. This means that after 4 years, the husband's age will be 9y and the wife's age will be 7y (where y is a constant).
So we can set up the equation:
4x + 4 = 9y
3x + 4 = 7y
Simplifying the equations, we have:
4x - 9y = -4 (Equation 1)
3x - 7y = -4 (Equation 2)
To solve these equations, we can use a method called substitution.
From Equation 1, we can express x in terms of y:
x = (9y - 4)/4
Substituting this into Equation 2, we have:
3((9y - 4)/4) - 7y = -4
Simplifying this equation, we get:
(27y - 12)/4 - 7y = -4
Multiplying through by 4 to eliminate the fraction, we get:
27y - 12 - 28y = -16
Combining like terms, we have:
-y - 12 = -16
Adding 12 to both sides, we get:
-y = -4
Multiplying through by -1 to isolate y, we have:
y = 4
Now that we have the value of y, we can substitute it back into either Equation 1 or Equation 2 to solve for x.
Let's use Equation 1:
4x - 9(4) = -4
Simplifying, we get:
4x - 36 = -4
Adding 36 to both sides, we have:
4x = 32
Dividing through by 4, we get:
x = 8
Now that we have the values of x and y, we can determine the current ages of the husband and wife:
Husband's current age = 4x = 4 * 8 = 32 years
Wife's current age = 3x = 3 * 8 = 24 years
To find out how many years ago they got married, we need to subtract the current ages from the ages at the time of marriage.
According to the information given, the ratio of their ages at the time of marriage was 5:3. This means that the husband's age at the time of marriage was (5/8) * 32 = 20 years, and the wife's age was (3/8) * 32 = 12 years.
To find out how many years ago they got married, we subtract the ages at the time of marriage from their current ages:
Years ago = Current age - Age at the time of marriage
= 32 - 20 = 12
Therefore, they got married 12 years ago.
To find out how many years ago the couple got married, we can set up equations based on the given information.
Let's assume that the husband's age at the time of marriage was 5x years, and the wife's age was 3x years.
According to the first statement, the ratio of their ages after 4 years will be 9:7. This means that 4 years after the present time, the husband will be 4x + 4 years old, and the wife will be 3x + 4 years old. So, the equation we can set up is:
(4x + 4) / (3x + 4) = 9/7
Cross-multiplying, we get:
7(4x + 4) = 9(3x + 4)
28x + 28 = 27x + 36
28x - 27x = 36 - 28
x = 8
So, the husband's current age is 5x = 5 * 8 = 40 years old, and the wife's current age is 3x = 3 * 8 = 24 years old.
Now, we can calculate how many years ago they got married by subtracting the current age from the total years of marriage. The total years of marriage is the difference between the husband's and wife's ages at the time of marriage:
Total years of marriage = 5x - 3x = 2x = 2 * 8 = 16 years
Therefore, they got married 16 years ago.