Question

The difference in the ages of a father and son is 30 years and the difference of the squares of their ages is 1560. find their ages.

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Answer 1

Answer:

• Age of son = 11 years
• Age of father = 41 years

Explanation:

Given:

• Difference between ages of father and son = 30 years
• Difference of square of their ages = 1560

To Find:

• Their ages.

Let,

• Age of son = 'x'
• Age of father = 'x + 30'

Now, according to question,

⇒ (x + 30)² - (x)² = 1560

⇒ x² + 900 + 60x - x² = 1560

⇒ 900 + 60x = 1560

⇒ 60x = 1560 - 900

⇒ 60x = 660

⇒ x = 660/60

⇒ x = 11

Hence,

• Age of son = 11 years
• Age of father = 11 + 30 = 41 years

Verification:

⇒ (41)² - (11)² = 1560

⇒ 1681 - 121 = 1560

⇒ 1560 = 1560

Hence Verified!!

Answer 2

Let the age of son be x

so the age of father =x+30

so by the condition given in your question we get equation

(x+30)^2-(x)^2=1560

x^2+60x+900-x^2=1560

60x+900=1560

60x=660

x=11 years

x+30=11+30=41 years

so age of son is 11 years and age of father is 41 years