LCM and HCF Practice Test 2

Question : 35 of 40

Marks: +1, -0

The L.C.M. of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then find their difference.

Solution:

Let the number be x and

(100 - x)

Now,

x (100 - x) = 5 × 495

⇒ x^2 - 100x + 2475 = 0

⇒ x^2 - 55x - 45x + 2475 = 0

⇒ x (x- 55) - 45 (x - 55) = 0

⇒ (x - 45) (x -55) = 0

Either,

x = 45 \or, x = 55

Hence, the numbers are 45 and 55
So, their difference = 55 – 45 = 10

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