Question

116.
Present age of father is 28 years
more than his son's age. Father's
age becomes 2 times of his son's
age after 20 years. Then what is
the present age of the father ?
1) 36 years
2)
38 years
3)
8 years
4)
28 years​

Answer 1

Answer: Option A)

Steps:

Let the present age of son be 'x' years. Hence the present age of father according to the question is:

• Age of father (present) = ( x + 28 ) years

Also, it is given that father's age would become 2 times of his son's age after 20 years.

• ⇒ Father's age + 20 years = 2 ( x + 20 )

Substituting Father's age from previous equation in the latest equation we get:

→ ( x + 28 + 20 ) = 2 ( x + 20 )

→ ( x + 48 ) = 2x + 40

→ 2x - x = 48 - 40

→ x = 8 years

Hence the present age of Son is 8 years.

Hence the present age of father is:

→ 8 + 28 = 36 years

Hence the present age of the father is 36 years.

Hence Option A) is the correct answer.

Answer 2

Answer:

Given :-

• Present age of father is 28 years more than his son's age.
• Father's age becomes 2 times of his son's age after 20 years.

To Find :-

• What is the present age of the father.

Solution :-

» Let, the present age of son be x

» And, the present age of father will be x + 28

➙ After 20 years,

» Then, the age of son is x + 20

» And, the age of his father's will be 2(x + 20)

According to the question,

⇒ (x + 28) + 20 = 2(x + 20)

⇒ x + 28 + 20 = 2x + 40

⇒ x + 48 = 2x + 40

⇒ x - 2x = 40 - 48

⇒ - x = - 8

➠ x = 8

Hence, the required age of his son and his father will be,

✦ Age of son = x = 20 years

✦ Age of his father = x + 28 = 8 + 28 = 36 years

∴ The age of father is 36 years .

Hence, the correct options is option no (1) 36 years .

Let's Verify :-

⇒ (x + 28) + 20 = 2(x + 20)

Put the value of x = 8 we get,

⇒ (8 + 28) + 20 = 2(8 + 20)

⇒ 8 + 28 + 20 = 16 + 40

⇒ 56 = 56

➥ LHS = RHS

Hence, Verified ✔