When the son will be as old as the father today their ages will add up to 126 years.When the father was old as the son is today,their ages add upto 38 years,Find their present ages.
Answers
When the son will be as old as the father today, son's age will be his farther's age = x years.
Thus, the sum of the ages = x + x = 126
Therefore, x = 126/2 = 63 years
Similarly, When the father was old as the son is today, father's age will be his son's age = y years.
Thus, the sum of the ages = y + y = 38
Therefore, y = 38/2 = 19 years.
The present age of father is 63 years and present age of son is 19 years.
Answer:
Age of Son = 30 years old, Age of Father = 52 years old
Hint: The Father and Son both age accordingly.
Example: Son = 15yrs, Father = 40yrs. If Son becomes 17 ( 15+2 ) then Father becomes 42 ( 40+2 )
Step-by-step explanation:
Let,
Son's current age = x
Father's current age = y
Difference between Age of Father and Son = x - y
Case 1: When Son become Father's current Age (and the Father becomes the number of years taken by the Son to reach the Fathers current Age, i.e., The difference between their ages + Father's Current Age)
[Father's new age] + [Son's new age] = 126
[ y + (y−x) ] + [ x + (y−x) ] = 126
⇒ (2y−x) + (y) = 126
∴ 3y−x = 126 -----> (1)
Case 2: When Father become Son's current Age (and the Son becomes the number of years deducted by the Father to reach the Son's current Age, i.e., The difference between their ages - Son's Current Age)
[Father's previous age] + [Son's previous age] = 38
[ y − (y−x) ] + [ x − (y−x) ] = 38
⇒ (x+x) + (−y+x) = 38
⇒ ( −y+3x = 38 ) x 3 (For fulfilling Elimination Method Criteria)
∴ −3y+9x = 114 -----> (2)
Using Elimination Method,
−3y + 9x = 114 -----> (2)
3y − x = 126 -----> (1)
(2)-(1)⇒ 8x = 240
∴ x = 240/8 = 30 yrs
Put x = 30 in eqn (1),
3y − x = 126
3y − 30 = 126
3y = 126 + 30 = 156
∴ y = 156/3 = 52 yrs
The son is 30 yrs old and the father is 52 yrs old.