The LCM of two numbers is 385 and their HCF is 7. If the sum of the two numbers is 112, then their difference is:

Correct option is C

Given:

LCM = 385

HCF = 7

Sum of the numbers = 112

Formula used:

The product of two number is: LCM × HCF 

The formula of difference between the number is: $$\sqrt{(x + y)^2 - 4(x \times y)}.$$ 

Solution:

Let be the two numbers is $$x$$ and $$y$$​​

The product of two no is = 385 × 7 = 2695

$$\text{Difference} = \sqrt{(x + y)^2 - 4(x \times y)}$$

                    $$= \sqrt{112^2 - 4 \times 2695}$$ = $$\sqrt{12544 - 10780}$$ = $$\sqrt{1764}$$  = 42

Thus the correct answer is (C)

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