Question
The 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:Solution
Let the two numbers be 11x and 11y (HCF = 11) Given: 11x + 11y = 132 ⇒ x + y = 12 Also, both numbers > 42 ⇒ 11x > 42 and 11y > 42 ⇒ x > 3.8 and y > 3.8 Possible integer pair with sum 12 and both > 3.8: x = 5, y = 7 Numbers are: 11 × 5 = 55 11 × 7 = 77 Difference = 77 − 55 = 22
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