A man's age is 4 times the combined age of a two sons. One of whom is 3 times as old as the other. In 24 years their combined ages will be 12 year less than their father's age . Find their respective age ????
X Yrs old = Age of one son.
3x yrs old = Age of other son.
4(x+3x) = 16x = Age of the father.
(x+24) + (3x+24) = (16x+24) - 12.
4x + 48 = 16x + 12
4x - 16x = 12 - 48
-12x = -36
X = 3
x+24 = 3+24 = 27 Yrs=Youngest son's age,
3x+24 = 9+24 = 33 Yrs=Oldest son's age.
16x+24 = 48+24=72 Yrs=The father's age.
To solve this problem, let's assign variables to the unknowns. Let's call the father's age "F," the age of the older son "O," and the age of the younger son "Y."
We are given the following information:
1. The father's age is 4 times the combined age of the two sons:
F = 4(O + Y)
2. One of the sons is 3 times as old as the other:
O = 3Y
3. In 24 years, their combined ages will be 12 years less than their father's age:
(O + 24) + (Y + 24) = F + 12
Now, we can solve the problem using these equations.
1. Substitute O = 3Y into the first equation:
F = 4(3Y + Y)
F = 4(4Y)
F = 16Y
2. Substitute F = 16Y into the third equation:
(3Y + 24) + (Y + 24) = 16Y + 12
4Y + 48 = 16Y + 12
4Y - 16Y = 12 - 48
-12Y = -36
Y = -36 / -12
Y = 3
3. Substitute Y = 3 into the second equation to find O:
O = 3(3)
O = 9
So, the younger son is 3 years old (Y = 3) and the older son is 9 years old (O = 9). To find the father's age, substitute Y = 3 into the first equation:
F = 16(3)
F = 48
Therefore, the father's age is 48.