five years ago Mr. arun was five times old as his son and five years hence he would be eight years less thrice the corresponding age of his son . find their present age and verify your answer.
Answers
Answer :
- The present age of Mr.Arun = 35 years
- The present age of his son = 11 years
Step-by-step explanation :
Let the present age of Arun's son be x years
and the present age of Arun be y years
Five years ago,
Arun's age = (y - 5) years
His son's age = (x - 5) years
Given, Mr. arun was five times old as his son
y - 5 = 5(x - 5)
y - 5 = 5x - 25
5x - y = 25 - 5
5x - y = 20
y = 5x - 20 --- [ 1 ]
Five years hence,
Arun's age = (y + 5) years
His son's age = (x + 5) years
Given, Mr.Arun would be eight years less thrice the corresponding age of his son.
y + 5 = 3(x + 5) - 8
y + 5 = 3x + 15 - 8
y + 5 = 3x + 7
y - 3x = 7 - 5
y - 3x = 2 --- [ 2 ]
Substitute equation [1] in equation [2]
y - 3x = 2
5x - 20 - 3x = 2
5x - 3x = 20 + 2
2x = 22
x = 22/2
x = 11
Substitute the value of x in equation [ 1 ]
y - 3x = 2
y - 3(11) = 2
y - 33 = 2
y = 33 + 2
y = 35
The present age of Mr.Arun = 35 years
The present age of his son = 11 years
Verification :
Condition - 1 :
Five years ago,
Mr.Arun's age = 35 - 5
= 30 years
His son's age = 11 - 5
= 6 years
Mr.Arun's age = 5 × (His son's age)
30 = 5 × 6
30 = 30
Condition - 2 :
After five years,
Mr.Arun's age = 35 + 5
= 40 years
His son's age = 11 + 5
= 16 years
Mr.Arun's age = 3(his son's age) - 8
40 = 3(16) - 8
40 = 48 - 8
40 = 40
Hence verified!!
Answer:
ARUN'S. AGE = 60 YEARS
SON'S AGE = 40 YEARS