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Question
The ratio of two numbers is 3:2 and the difference of their square is 500. Find the numbers.
Solution
Given: Ratio of two numbers = 3:2
So, let the two numbers be 3x and 2x.
Now, according to the question,
(3x)2 – (2x)2 = 500
⇒ 9x2 – 4x2 = 500
⇒ 5x2 = 500
⇒ x2 = `500/5` = 100
⇒ x = `sqrt(100)`
⇒ x = ± 10
For x = – 10,
First number = 3 × (– 10) = – 30
and second number = 2 × (–10) = – 20
For x = 10,
First number = 3 × (10) = 30
and second number = 2 × (10) = 20
Hence, the numbers are – 30, – 20 or 30, 20.
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