NIELIT 2016 DEC Scientist B - Section A: 43

Question

The $LCM$ of two numbers is $45$ times their $HCF$. If the sum of the $LCM$ and the $HCF$ of these two numbers is $1150$ and one of the numbers is $125$, then the other number is :

• A. $256$
• B. $225$
• C. $250$
• D. $255$

Answer 1

Given that, $LCM = 45 \times HCF \quad\rightarrow(1)$

and, $LCM + HCF = 1150\quad\rightarrow(2)$

Now, put the value from the equation $(1)$ of $LCM$ in the equation $(2),$ then we get

$45 \times HCF + HCF = 1150$

$\implies 46HCF = 1150$

$\implies HCF = 25,\;LCM = 1125$

We know that, $\text{First number} \times \text{Second number} = \text{LCM} \times \text{HCF}$

$\implies 125 \times \text{Second number}  = 1125 \times 25$

$\implies \text{Second number}  = 225$

So, the correct answer is $(B).$