Question

Construct a word problem on quadratic equation, such that one of its answers is 20 (years, rupees, centimeter, etc.). Also, solve it.

Answer 1

Word Problem:

The sum of the ages of a father and his son is 56 years. Four years ago, the square of the son's age was equal to the father's age at that time. Find their present ages.

Let the son’s present age be x years.

Then the father’s present age is 56 − x years.

Four years ago:

• Son’s age = x − 4

• Father’s age = 56 − x − 4 = 52 − x

(Son’s age 4 years ago)² = Father’s age 4 years ago

(x − 4)² = 52 − x

x² − 8x + 16 = 52 − x

x² − 7x + 16 − 52 = 0

x² − 7x − 36 = 0

(x − 12) (x + 3) = 0 ⇒ x = 12 or x = −3

x = 12 ⇒ Son’s present age = 12 years

Father’s present age = 56 − 12 = 44 years

Son = 8 years → 82 = 64

Father = 44 − 4 = 40 → Not equal!

Let the breadth be x meters.
Then length = x + 4 meters.

Area = x (x + 4) = 400

x² + 4x = 400 ⇒ x² + 4x − 400 = 0

`x = (-4 +- sqrt(16+1600))/2 = (-4 +- sqrt1616)/2`

x² + 4x − 400 = 0 ⇒ (x − 20) (x + 20) = 0 ⇒ x = 20 or x = −20

x = 20 meters 

Length = 24 meters