Question : The sum of two positive numbers is 240 and their HCF is 15. Find the number of pairs of numbers satisfying the given condition.
Option 1: 5
Option 2: 2
Option 3: 8
Option 4: 4
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Correct Answer: 4
Solution :
Given: The sum of two positive numbers is 240 and their HCF is 15.
Let $x$ and $y$ be two coprime then the numbers are $15x$ and $15y$.
According to the question,
$15x+15y=240$
⇒ $x+y=16$
The number of pairs of numbers satisfying the given condition = 4 i.e. (1, 15), (3, 13), (5, 11), and (7, 9).
Hence, the correct answer is 4.
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