The sum of the ages of a father and his two sons is 52 years. One son is older than the other by 3 years. When the age of the older son will be same as the present age of the father, the sum of the ages of the three will be 136 years. Find each of their present ages.
Answers
Answer:
The sum of the ages of a father and his two sons is 52 years.
One son is older than the other by 3 years.
When the age of the older son will be the same as the present age of the father, the sum of the ages of the three will be 136 years.
To find:
Find each of their present ages.
Solution:
Let, father's age = x
Let, younger son's age = y
So, the age of elder son = y + 3
Sum of their ages = 52
x + y + (y + 3) = 52
x + 2y = 52 - 3
x + 2y = 49
x = 49 - 2y
After T years, the age of the older son will be the same as the present age of the father.
So, After T years, the age of the elder son = y + 3 + T
So, y + 3 + T = x = 49 - 2y
y + 3 + T = 49 - 2y
T = 49 - 2y - y - 3
T = 46 - 3y
So, after 46 - 3y years the age of the older son will be the same as the present age of the father.
So,
Age of father after 46 - 3y years = (49 - 2y) + (46 - 3y) = 95 - 5y
Age of younger son after 46 - 3y years = y + (46 - 3y) = 46 - 2y
Age of older son after 46 - 3y years = (y + 3) + (46 - 3y) = 49 - 2y
So, (95 - 5y) + (46 - 2y) + (49 - 2y) = 136
190 - 9y = 136
9y = 190 - 136
9y = 54
y = 6
The present age of younger son = y = 6 years
The present age of older son = y + 3 = 6 + 3 = 9 years
The present age of father = x = 49 - 2y = 49 - 2(6) = 49 - 12 = 37 years
Given :- The sum of the ages of a father and his two sons is 52 years. One son is older than the other by 3 years. When the age of the older son will be same as the present age of the father, the sum of the ages of the three will be 136 years.
To Find :-
- Find each of their present ages. ?
Answer :-
→ Let present age of father is F years , Elder son is E years and younger son is Y years .
so,
→ F + E + Y = 52 ------ Eqn.(1)
→ E - Y = 3 ------ Eqn.(2)
→ (F + F - E) + (E + F - E) + (Y + F - E) = 136
→ 2F - E + F + F - E + Y = 136
→ 4F - 2E + Y = 136 ------ Eqn.(3)
multiply Eqn.(1) by 4 and subtracting Eqn.(3) from that,
→ 4(F + E + Y) - (4F - 2E + Y) = 52*4 - 136
→ 4F - 4F + 4E + 2E + 4Y - Y = 72
→ 6E + 3Y = 72
→ 2E + Y = 24 ------- Eqn.(4)
putting value of E from Eqn.(2) in Eqn.(4) now,
→ 2(3 + Y) + Y = 24
→ 6 + 3Y = 24
→ 3Y = 18
→ Y = 6 years .
Putting value of Y in Eqn.(2)
→ E - 6 = 3
→ E = 9 years .
putting values of E and Y in Eqn.(1),
→ F + 9 + 6 = 52
→ F = 52 - 15
→ F = 37 years .
Learn more :-
few children go to a park, if each child sits alone on a bench, there is one child left standing and if two children occ...
https://brainly.in/question/37181989