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The LCM and HCF of two positive numbers are 175 and 5 respectively. If the sum of the numbers is 60, what is the difference between them ? |
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Answer» Let the two numbers be 5a and 5b as HCF of the two numbers = 5 ∴ Product of the two number = HCF × LCM ⇒ 5a × 5b = 5 × 175 ⇒ ab = \(\frac{175}{5}=35\) (a, b) can be (1, 35) or (5, 7) Thus, the numbers can be (1 × 5 and 35 × 5) or (5 × 5 and 5 × 7), i.e., (5 and 175) or (25 and 35) The sum = 60 is satisfied by the pair (25, 35). Hence, the difference of the numbers is 10. |
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