Question
Download Solution PDFThe sum of two positive numbers is 240 and their HCF is 15. Find the number of pairs of numbers satisfying the given condition.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The sum of two number positive number is 240 and their HCF is 15.
Calculation:
Let two positive number is 15x and 15y where x and y should be coprime that means x and y should have HCH as 1.
According to the question
The sum of the number is
⇒ 15x + 15y = 240
⇒ x + y = 16
Now, we have to find the number of pair in which sum of the two number is 16 but no common factor between them, such pair is
⇒ (1, 15) (3, 13) (5, 11) (7, 9)
∴ Total possible pairs is 4.
Confusion Points
We can't take (2, 14), (4, 12), (6, 10), (8, 8) Because In these cases the pair should be co-prime.
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