When the son's age will be as his father's age sum of their ages will be 126 and when his father was at his son's age sum of their ages was 38.Find their present ages.
Answers
Answer:
correct answer is given below
Step-by-step explanation:
Let son 's current age is x and father 's current age is y.
Where does the(y-x) term come from? Well, it says 'when the son will be as old as the father is today, which means that the son has to age a certain amount of years. How many years does he have to age? The difference between his current age and his father 's current age.
For example, if the son was 10 and the father was 40, it would take the son 30 years (or y-x = 40-10) to reach his current age. In the meantime, the father would age the same amount (y - x = 40 - 10 = 30 years).
[Father 's new age] + [Son 's new age] = 126
[y+(y-x)] + [(x + (y-x))] = 126
⇒ 2y - x + y = 126
∴ 3y - x = 126 ----------(1)
[Father 's previous age] + [Son 's previous age] = 38
⇒ [y - (y-x)] + [x - (y-x)] = 38
⇒ x + x - y + x = 38
⇒ 3x - y = 38
∴ y = 3x - 38 -----------(2)
Now sub equ(2) into equation 1
⇒ 3(3x-38) - x = 126
⇒ 9x - 114 - x = 126
⇒ 8x = 240
∴ x = 30
Now y = 3x - 38
⇒ y = 3(30) - 38
∴ y = 52
The son is 30 years old, and the father is 52 years old.
Step-by-step explanation:
The age difference will remain always constant.
Let the age difference be k years.
And age of father and his son be x and y years respectively.
x-y=k....(1)
Son will be age of his father when the age difference is added.
That is y+k=x
x+k+x=126...(2)
(Substituting equation(1) in equation(2) )
x+(x-y)+x=126
3x-y=126...(3)
Father will be as the age of his son when age difference is subracted.
That is x-k=y
y+y-k=38
(substituting equation(1) )
y+y-(x-y)=38
-x+3y=38...(4)
(multiply eq(4) by 3 )
-3 +9y=114...(5)
(add equations (3) and (5) )
3x-y=126
+
-3x+9y=114
we get,
8y=240
y=240/8
y=30
( substituting y=30 in eq(3) )
3x-30=126
3x=126+30
3x=156
x=156/3
x=52
Therefore present ages of father and his son are 52 and 30 respectively.