Problems on H.C.F and L.C.M - Quantitative Aptitude (MCQ) questions for Q. 100

Q.  LCM of two numbers is 495. HCF of these numbers is 5. If the sum of the numbers is 100, find out the difference between the two numbers.
- Published on 15 Jun 15

a. 15
b. 12
c. 10
d. 20

ANSWER: 10
 
It is given that sum of two numbers is 100. Let the two numbers be x and 100 – x and HCF is 5 and LCM is 495

=> We need to apply the formula: HCF x LCM = Product of two numbers

Which gives x(100 – x) = 495 x 5

Solving the equation we get a quadratic which looks like this:

x2 – 100x + 2475 = 0

=> (x – 55)(x- 45) = 0

Therefore, Two numbers are 55 and 45

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