Question
Download Solution PDFThe HCF of two numbers is 11 and their sum is 132. If both the numbers are greater than 42, then the difference between the two numbers is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
HCF = 11
Sum = 132
Numbers > 42
Formula Used:
Let the numbers be 11x and 11y, where x and y are co-prime integers.
Sum of numbers = 11x + 11y
Difference of numbers = |11x - 11y|
Calculation:
11x + 11y = 132
⇒ 11(x + y) = 132
⇒ x + y = 132 / 11 = 12
Possible co-prime pairs (x, y) such that x + y = 12 are (1, 11) and (5, 7).
Case 1: x = 1, y = 11
Numbers are 11 × 1 = 11 and 11 × 11 = 121. (11 is not > 42, so this case is rejected)
Case 2: x = 5, y = 7
Numbers are 11 × 5 = 55 and 11 × 7 = 77. (Both are > 42)
Difference = |55 - 77|
⇒ Difference = |-22|
⇒ Difference = 22
∴ The difference between the two numbers is 22.
Last updated on Jul 8, 2025
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