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Question
Two natural numbers are in the ratio 3 : 4. Find the numbers if the difference between their squares is 175.
Solution
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 = `(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.
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