Question
Download Solution PDFThe sum of the two numbers is 36 and their HCF is 4. How many pairs of these numbers are possible?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The sum of the two numbers is 36 and their HCF is 4.
Formula used:
Let the two numbers be 4a and 4b, where a and b are co-prime (HCF is 1).
We know, 4a + 4b = 36
Calculation:
4a + 4b = 36
⇒ a + b = 9
Possible pairs (a, b) such that a and b are co-prime:
1. (1, 8)
2. (2, 7)
3. (4, 5)
Thus, the pairs of numbers are:
1. (4×1, 4×8) = (4, 32)
2. (4×2, 4×7) = (8, 28)
3. (4×4, 4×5) = (16, 20)
∴ The correct answer is 3.
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