The present ages of a man and his wife are as 6:4. Five years ago their ages were in the ratio 5:3. What is the age gap of the couple?
m/w = 6/4
(m-5)/(w-5) = 5/3
(m,w) = (30,20)
m-w = 10
Let's assume the present age of the man is 6x and the present age of his wife is 4x.
According to the given information, five years ago their ages were in the ratio 5:3. So, we can write the equation:
(6x - 5) / (4x - 5) = 5/3
Cross-multiplying the equation, we get:
3(6x - 5) = 5(4x - 5)
18x - 15 = 20x - 25
Moving the variables to one side and the constants to the other, we get:
20x - 18x = 25 - 15
2x = 10
Dividing both sides by 2, we find:
x = 5
Now, we can find the present ages of the man and his wife:
Age of the man = 6x = 6 * 5 = 30 years
Age of the wife = 4x = 4 * 5 = 20 years
The age gap between the man and his wife is:
30 - 20 = 10 years
Therefore, the age gap between the couple is 10 years.
To find the age gap between the man and his wife, we first need to determine their present ages.
Let's assume the present age of the man is 6x and the present age of his wife is 4x (since their ages are in the ratio 6:4).
Now, we are given that five years ago, their ages were in the ratio 5:3. So, we need to subtract 5 from both their ages and set up the following equation:
(6x - 5) / (4x - 5) = 5/3
We can cross-multiply to solve for x:
3(6x - 5) = 5(4x - 5)
18x - 15 = 20x - 25
18x - 20x = -25 + 15
-2x = -10
x = -10 / -2
x = 5
Now that we have found the value of x, we can substitute it back in to find their present ages:
Man's age = 6x = 6 * 5 = 30
Wife's age = 4x = 4 * 5 = 20
So, the present age of the man is 30 and the present age of the wife is 20.
To find the age gap between them, we subtract the wife's age from the man's age:
Age gap = Man's age - Wife's age
= 30 - 20
= 10
Therefore, the age gap between the man and his wife is 10 years.