4 years ago my father's age was 4 times that of my age. At present the sum of my father's age and that of mine is 53 years . What is father's present age.
40 Year,13year
Let's assign variables to represent the ages mentioned in the problem. Let "x" be your father's present age and "y" be your present age.
From the problem, we can form two equations:
1. "4 years ago my father's age was 4 times that of my age":
(x - 4) = 4(y - 4)
2. "At present the sum of my father's age and that of mine is 53 years":
x + y = 53
Let's solve the second equation for x:
x = 53 - y
Substitute this value of x into the first equation:
(53 - y - 4) = 4(y - 4)
Simplify the equation:
49 - y = 4y - 16
Combine like terms:
5y = 49 + 16
5y = 65
Divide both sides by 5:
y = 13
Substitute the value of y back into x = 53 - y:
x = 53 - 13
x = 40
Therefore, your father's present age is 40.
To solve this problem, let's start by using algebraic expressions.
Let's assume your father's present age is 'F' and your age is 'M'.
According to the problem, 4 years ago, your father's age was 4 times your age. So we can write the equation:
F - 4 = 4(M - 4)
Now, we're given that the sum of your father's age and your age is 53 years. So we can write another equation:
F + M = 53
Now we have a system of two equations and two variables. We can solve for F by substitution.
Rearrange the second equation to solve for one variable in terms of the other:
M = 53 - F
Substitute this value of M in the first equation:
F - 4 = 4((53 - F) - 4)
Simplify the equation:
F - 4 = 4(49 - F)
Distribute the 4:
F - 4 = 196 - 4F
Combine like terms:
5F - 4 = 196
Add 4 to both sides:
5F = 200
Divide by 5:
F = 40
So, your father's present age is 40 years.
father's age is f. My age is m.
(f-4) = 4(m-4)
f+m = 53
Now just solve for f and m.