5. Seven years hence, Anugrah's father will be nine more than twice the age of his son. Five years ago, his father was five more than four times his son's age. What are their present ages? *
Answers
Answer:
- 13 and 42 years are the present ages of son and father.
Step-by-step explanation:
Given
- Seven years hence, Anugrah's father will be nine more than twice the age of his son.
- Five years ago, his father was five more than four times his son's age.
To find
- Their present ages.
Solution
➝ Let the present age of Anugrah's father be x years.
➝ And present age of Anugrah be y years.
➝ Seven years hence (after):
- Anugrah's father = x + 7
- Anugrah = y + 7
➝ According to the condition:
Seven years hence, Anugrah's father will be nine more than twice the age of his son.
- (x + 7) - 9 = 2(y + 7)
- x + 7 - 9 = 2y + 14
- x - 2 = 2y + 14
- x - 2y = 16 - (i)
➝ Five years ago (before):
- Anugrah's father = x - 5
- Anugrah = y - 5
➝ According to the condition:
5 years ago, Anugrah's father was five more than four times his son age.
- (x - 5) - 5 = 4(y - 5)
- x - 5 - 5 = 4y - 20
- x - 10 = 4y - 20
- x - 4y = -10 - (ii)
➝ Substract the future age from past age.
➝ Substract (i) from (ii).
- (x - 4y) - (x - 2y) = -10 - 16
- x - 4y - x + 2y = -26
- -2y = -26
- y = 13
➝ Substitute y = 8 in (i).
- x - 2y = 16
- x - 2(13) = 16
- x - 26 = 16
- x = 42
Verification
- x - 2y = 16
- 42 - 2(13) = 16
- 42 - 26 = 16
- 16 = 16
➝ L.H.S = R.H.S
- x - 4y = -10
- 42 - 4(13) = -10
- 42 - 52 = -10
- -10 = -10
➝ L.H.S = R.H.S
Answer:
- Anugrah's present age = 13 years
- Anugrah's father's present age = 42 years
Solution:
Let the present age of Anugrah's father and Anugrah be x and y years.
According to the question, There are two cases which will give two different linear equations. The value of x and y that satisfy both the equations will be the age of the two person.
Case 1:
After seven years, Anugrah's father will be nine more than twice the age of his son.
This can be expressed in terms of x and y as,
⇒ (Age of anugrah's father 7 years later) - 9 = 2 × (Anugrah's age 7 years later)
⇒ (x + 7) - 9 = 2(y + 7)
⇒ x + 7 - 9 = 2y + 14
⇒ x - 2y = 14 + 9 - 7
⇒ x - 2y = 16 ...(i)
NOTE: 7 is being added to their present ages because the given condition is of 7 years later and at that time both will be 7 years older as that of now.
Case 2:
5 years ago, Anugrah's father was five more than four times his son's (Anugrah) age.
Similarly, This can be written as,
⇒ (Age of Anugrah's father 5 years ago) - 5 = 4 × (Age of Anugrah 5 years ago)
⇒ (x - 5) - 5 = 4(y - 5)
⇒ x - 5 - 5 = 4y - 20
⇒ x - 4y = -20 + 10
⇒ x - 4y = -10 ...(ii)
NOTE: Similarly, In the second case, 5 will be subtracted from their ages as the given condition is of 5 years ago and at that time they were 5 years younger as that of now.
Subtracting eq.(i) from eq.(ii),
⇒ (x - 4y) - (x - 2y) = -10 - 16
⇒ x - 4y - x + 2y = -26
⇒ -2y = -26
⇒ y = 13
Now, Substitute (y = 13) in eq.(i),
⇒ x - 2(13) = 16
⇒ x - 26 = 16
⇒ x = 42
Hence, The present age of Anugrah is 13 years and Anugrah's father is 42 years.