the sum of son and fathers age is 74 years.the ratio of their age was 7:2 since 10 years ago.what is the ratio of their age will stand after 10 year
s+f = 74
(f-10)/(s-10) = 7/2
So, solve for s and f, and then evaluate
(f+10)/(s+10)
To solve this problem, we can use a system of equations. Let's represent the son's current age as "x" and the father's current age as "y."
According to the given information, the sum of their ages is 74 years:
x + y = 74 ...(Equation 1)
The ratio of their ages 10 years ago was 7:2. We can express their ages 10 years ago as "x - 10" and "y - 10":
(x - 10) / (y - 10) = 7/2
Now, let's solve the first equation for "x":
x = 74 - y ...(Equation 2)
Substituting Equation 2 into the second equation:
(74 - y - 10) / (y - 10) = 7/2
Simplifying the equation:
(64 - y) / (y - 10) = 7/2
Cross-multiplying:
2(64 - y) = 7(y - 10)
128 - 2y = 7y - 70
Rearranging and combining like terms:
9y = 198
Dividing both sides by 9:
y = 22
Now, substitute the value of "y" back into Equation 2 to find "x":
x = 74 - 22
x = 52
Therefore, the son's current age is 52 and the father's current age is 22.
Now, let's find the ratio of their ages after 10 years.
After 10 years, the son's age will be 52 + 10 = 62, and the father's age will be 22 + 10 = 32.
The ratio of their ages will be 62:32, which can be simplified as 31:16.
So, the ratio of their ages after 10 years will be 31:16.