Question

Ram is half of his father's age. 20 years ago, the age of his father was 6 times the age of Ram. Find the age of Ram and his father.
A. Ram = 30 years, Father = 60 years.
B. Ram = 25 years, Father = 50 years.
C. Ram = 22 years, Father = 44 years.
D. Ram = 20 years, Father = 40 years.

Answer 1

Hint: Let's assume that their present ages are x years and y years.
20 years ago, their ages were $ x-20 $ years and $ y-20 $ years respectively.
We can form equations using the given information and solve to get the values of x and y.

Complete step by step answer:
Let's say the current age of Ram is x years and that of his father is y years.
The various relations, between their ages is listed in the table below:

	Ram	Ram's Father	Relation
Current age:	$ x $	$ y $	$ x=\dfrac{1}{2}\times y $
20 years ago:	$ x-20 $	$ y-20 $	$ 6\times (x-20)=y-20 $

We have the following two equations:
 $ x=\dfrac{1}{2}\times y $ ... (1)
 $ 6\times (x-20)=y-20 $ ... (2)
On multiplying equation (1) by 2, we get:
 $ 2x=y $ ... (3)
Substituting this value of y in equation (2), we get:
 $ 6\times (x-20)=2x-20 $
⇒ $ 6x-120=2x-20 $
Subtracting 2x from both sides, we get:
⇒ $ 4x-120=-20 $
Adding 120 to both sides, we get:
⇒ $ 4x=100 $
Dividing both sides by 4, we get:
⇒ $ x=25 $
Using equation (3), we also get $ y=2\times 25=50 $ .

The correct answer is B. Ram = 25 years, Father = 50 years.

Note: The difference between people's age always remains a constant; currently, in the past or in the future. With increasing age (in the future), the ratio between the ages gets smaller. The question can also be solved by using only a single variable.