A father said to his son, "n years back I was as old as you are now. My present age is four times your age n years back". If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?
30 years
Let the age of father be X and the age of son be Y.
According to the question,
(X - n) = Y
Or X - Y = n ……….(i)
And X = 4(Y - n)
Or X = 4Y - 4n
Or (4Y - X)/4 = n ……….(ii)
From equations (i) and (ii), we get:
X - Y = (4Y - X)/4
Or 4X – 4Y = 4Y - X
Or 5X = 8Y
Or X/Y = 8/5
Or we can say that, X = 8k and Y = 5k
Given that, X + Y = 130
Or 8k +5k = 130
Or 13k = 130
Or k = 10
Hence, age of father (X) = 8k = 80 years
And age of son (Y) = 5k = 50 years
Difference in their ages = 80 – 50 = 30 years
30 years
Let:
Father's present age = \( F \)
Son's present age = \( S \)
From the statements:
- \( F - n = S \)
- \( F = 4(S - n) \)
- \( F + S = 130 \)
From (1): \( F = S + n \)
Substitute in (2):
\( S + n = 4(S - n) \Rightarrow 5n = 3S \Rightarrow S = \frac{5n}{3} \)
Now use equation (3):
\( 2S + n = 130 \Rightarrow 2\left(\frac{5n}{3}\right) + n = 130 \Rightarrow \frac{13n}{3} = 130 \Rightarrow n = 30 \)
So, \( S = 50 \), \( F = 80 \)
Difference of ages = \( 80 - 50 = 30 \) years
Answer:
30 years
30 years
Let F = Father's current age
Let S = Son's current age
From first statement:
F - n = S ⇒ F = S + n ...(1)
From second statement:
F = 4 × (S - n) ...(2)
Substituting equation (1) into (2):
S + n = 4S - 4n
5n = 3S ⇒ n = (3/5)S ...(3)
Given sum of ages:
F + S = 130
Using equation (1): (S + n) + S = 130
2S + n = 130
Substituting n from equation (3): 2S + (3/5)S = 130
(13/5)S = 130 ⇒ S = 50
Calculating n: n = (3/5) × 50 = 30
Father's age F = 50 + 30 = 80
Age difference:
F - S = 80 - 50 = 30 years
Final Answer:
\[ \boxed{30} \]
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When a child reaches adolescence, there is apt to be a conflict between the parents and the child, since
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they express, however, are so dogmatic that the young seldom confide in them, and usually go their
own way in secret.
