Question
If the sum of 2 numbers is 185, their LCM is 1700 and
HCF is 5. Then the difference between 2 numbers is:Solution
Let be the first number x then second (185 – x). By formula, ⇒ 1700 × 5 = x (185 – x) ⇒ 8500 = 185x – x2 ⇒ x2 – 185x + 8500 = 0 ⇒ x2 – 100x – 85x + 8500 = 0 ⇒ x(x – 100) – 85(x – 100) = 0 ⇒ x = 100, x = 85 So first number 85 and second number 100. ∴ The difference between two numbers = 100 – 85 = 15
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