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Question
Two numbers are in the ratio 5 : 7 and the difference of their squares is 600. Find the numbers.
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Solution
Let the two numbers be 5x and 7x, since the ratio between them is 5:7
Now,
(7x)2 - (5x)2 = 600
⇒ 49x2 - 25x2 - 600
⇒ 24x2 - 600
⇒ x2 = 25
⇒ x = 5
∴ 5x = 25
7x = 35
Therefore, the two numbers are 25 and 35.
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