amit is 32 years younger than his father. 4 years ago his age was one fifth of his father age. find their present ages.
a = f - 32
a-4 = 1/5(f-4)
Substitute f-32 for a in the second equation and solve for a. Insert that value into the first equation to solve for f. Check by putting both values into the second equation.
Give the answer
To find Amit's present age and his father's present age, let's assign variables to their ages:
Let's assume Amit's present age is A
And let's assume his father's present age is F
From the given information, we can form two equations:
Equation 1: Amit is 32 years younger than his father
A = F - 32
Equation 2: Four years ago, Amit's age was one-fifth of his father's
(A - 4) = (1/5)(F - 4)
Now we have a system of two equations with two variables. We can solve this system using substitution or elimination.
Let's solve it using substitution:
Substitute the value of A from Equation 1 into Equation 2:
(F - 32 - 4) = (1/5)(F - 4)
Simplify and solve for F:
(F - 36) = (1/5)(F - 4)
Multiply both sides by 5 to eliminate the fraction:
5(F - 36) = F - 4
Distribute:
5F - 180 = F - 4
Combine like terms:
5F - F = 180 - 4
4F = 176
Divide by 4:
F = 44
Now that we have the father's present age, we can substitute this value back into Equation 1 to find Amit's present age:
A = F - 32
A = 44 - 32
A = 12
Therefore, Amit's present age is 12 and his father's present age is 44.