The HCF and the LCM of two numbers are 15 and 300. respectively. if the difference of the two numbers is 15. find the sum of those two numbers.

Correct option is C

Given:

HCF of the two numbers = 15

LCM of the two numbers = 300

The difference between the two numbers is 15 

Formula Used:

HCF × LCM = Product of numbers 

​$$(x+y)^2=(x-y)^2+4x×y$$ (identity)​

Solution:​

Let the two numbers be $x$ and $y$.

HCF (x,y) × LCM(x,y) = x × y 

Substituting the known values

​$$15×300=x×y$$ 

​$$4500=x×y$$

we know that x-y = 15 and x × y = 4500

Substituting these values in above identity 

​$$(x+y)^2=(15)^2+4 × 4500$$ 

​$$(x+y)^2=225+18000$$ 

​$$(x+y)^2=18225$$ ​

​$$x+y = \sqrt{18225} = 135$$ 

Thus, the sum of the two numbers is 135.

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