Question : The greater of the two numbers whose product is 900 and whose sum exceeds their difference by 30 is:
Option 1: 60
Option 2: 75
Option 3: 90
Option 4: 100
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Correct Answer: 60
Solution :
Let the numbers be $x$ and $y$ where $x > y$.
According to the question,
⇒ $(x + y) – (x – y) = 30$
⇒ $x + y–x + y = 30$
⇒ $y = \frac{30}{2} = 15$
Also, $xy = 900$
⇒ $15x = 900$
$\therefore x = \frac{900}{15} = 60$
Hence, the correct answer is 60.
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