Question

दो सख्याओ का ल.स. 495 तथा म. स. 5 है यदि उन सख्याओ का योग 100 है तो उनका अन्तर क्या होगा?

Answer 1

Let the numbers be a and b


LCM = 495

HCF = 5

We know that,

Product of numbers = LCM × HCF

=> Product of numbers = 495 × 5

=> ab = 2475 -----(1)

Now,

a + b = 100

=> a = 100 - b -------(2)

On Substituting equation 2 in 1, we get

=> (100 - b) b = 2475

=> 100b - b^2 = 2475

=> b^2 - 100b + 2475 = 0

=> b^2 - 45b - 55b +2475 = 0

=> b (b-45) - 55 (b - 45) = 0

=> (b-55) (b - 45) = 0


First number = 55

Second number = 45

Difference = 55 - 45

= 10

Answer 2

Let the numbers be a and b

LCM = 495

HCF = 5

We know that,

Product of numbers = LCM × HCF

=> Product of numbers = 495 × 5

=> ab = 2475 -----(1)

Now,

a + b = 100

=> a = 100 - b -------(2)

On Substituting equation 2 in 1, we get

=> (100 - b) b = 2475

=> 100b - b^2 = 2475

=> b^2 - 100b + 2475 = 0

=> b^2 - 45b - 55b +2475 = 0

=> b (b-45) - 55 (b - 45) = 0

=> (b-55) (b - 45) = 0

First number = 55

Second number = 45

Difference = 55 - 45

= 10

hope it helped ❤️