A father is twice as old as his daughter. If 20 years ago, the age of the father was 10 times the age of the daughter, what is the present age of the father?
by J Nandhini | Updated Sep 12, 2023
A father is twice as old as his daughter. If 20 years ago, the age of the father was 10 times the age of the daughter, what is the present age of the father?
Let's use algebra to solve this problem. Let the present age of the daughter be "D" years, and the present age of the father be "F" years.
According to the first statement, "a father is twice as old as his daughter," we can write:
F = 2D
Now, we have to consider the second statement, "20 years ago, the age of the father was 10 times the age of the daughter." This can be represented as:
(F - 20) = 10(D - 20)
Now, we have a system of two equations:
F = 2D
(F - 20) = 10(D - 20)
We can solve this system of equations to find the values of F and D.
First, substitute the value of F from equation 1 into equation 2:
(2D - 20) = 10(D - 20)
Now, distribute the 10 on the right side:
2D - 20 = 10D - 200
Next, move the 2D term to the left side by subtracting 2D from both sides:
-20 = 8D - 200
Now, add 200 to both sides to isolate the 8D term:
180 = 8D
Finally, divide both sides by 8 to find the value of
D = 180 / 8
D = 22.5
Now that we know the daughter's age is 22.5 years, we can find the father's age using equation 1:
F = 2D
F = 2 * 22.5
F = 45
So, the present age of the father is 45 years.
