The age of a man is twice the square of the age of his daughter. Eight years hence, the age of the man will be 4 years more than 3 times the age of his daughter. Find their present age.?

Question

Answer

Hey, here is your answer...

Suppose,
Daughter's present age = x years and man's present age = y years..

Then we have,

⇒y = 2x²
⇒y + 8 = 3(x + 8) + 4

substituting value of y from 1st equn. into 2nd equn...

⇒2x² + 8 = 3(x + 8) + 4
⇒2x² - 3x - 20 = 0
⇒(x - 4)(2x + 5) = 0

so,
either x = 4 or -5/2.

since, age cannot be negative,...

so, x = 4 and y = 2(4)² = 32.

That means the current age of daughter is 4 years and that of father is 32 years..

Hope this helps you.

Answer

Answer

Problem:

The age of a man is twice the square of the age of his daughter. Eight years hence, the age of the man will be 4 years more than 3 times the age of his daughter. Find their present age.

Solution:

Let's assume the present age of the daughter as x years.

Equations:

1. Age of the man = 2 * (age of the daughter)^2
2. Age of the man after 8 years = 3 * (age of the daughter after 8 years) + 4

Step 1:

Substituting the given values in equation 1, we get:

Age of the man = 2 * x^2

Step 2:

To find the age of the daughter after 8 years, we add 8 to her present age:

Age of the daughter after 8 years = x + 8

Step 3:

Substituting the values in equation 2, we get:

Age of the man after 8 years = 3 * (x + 8) + 4

Step 4:

Since the age of the man after 8 years is equal to the age of the man in equation 1 plus 8, we can equate the two expressions:

2 * x^2 + 8 = 3 * (x + 8) + 4

Step 5:

Simplifying the equation, we get:

2 * x^2 + 8 = 3x + 28 + 4

2 * x^2 - 3x - 24 = 0

Step 6:

Factoring the quadratic equation, we get:

(2x - 8)(x + 3) = 0

Step 7:

Setting each factor equal to zero and solving for x, we get:

2x - 8 = 0 or x + 3 = 0

x = 4 or x = -3

Since age cannot be negative, we discard x = -3.

Step 8:

Therefore, the present age of the daughter is 4 years.

Step 9:

Substituting the value of x in equation 1, we get:

Age of the man = 2 * (4)^2

Age of the man = 2 * 16

Age of the man = 32

Conclusion:

The present age of the man is 32 years and the present age of the daughter is 4 years.

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