Question

Two natural numbers are in the ratio 3 : 4. Find the numbers if the difference between their squares is 175.

Answer 1

Ratio in two natural numbers = 3 : 4
Let the numbers be 3x and 4x
According to the condition,
(4x)² - (3x)² = 175
⇒ 16x² - 9x² = 175
⇒ 7x² = 175

⇒ x² = ${\displaystyle \frac{175}{7}}$ = 25 = (±5)²
∴ x = 5, -5
But x - 5 is not a natural number
∴ x = 5
∴ Natural numbers are 3x, 4x
= 3 x 5, 4 x 5
= 15, 20.