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Given:
The L.C.M. of two numbers is 495 and their HCF is 5.
The sum of the two numbers is 100
Formula used:
Product of the two number = LCM × HCF
Calculation:
Let the one number be x and another number be 100 - x
According to the question,
⇒ x(100 - x) = 495 × 5
⇒ 100x - x2 = 2475
⇒ x2 - 100x + 2475 = 0
⇒ x2 - 55x - 45x + 2475 = 0
⇒ x(x - 55) - 45(x - 55) = 0
⇒ (x - 55)(x - 45) = 0
⇒ x = 55 or 45
If one number is 45 then another number 100 - 45 = 55
Or one number is 55 then another number 100 - 55 = 45
Their difference is 55 - 45 = 10
∴ Their difference is 10.
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