Question

The LCM of two numbers is fourteen times their HCF. The sum of HCF and Lcm is six hundred. If one number is two hundred eighty then the other number is.
A. Sixty
B. Fifty
C. Hundred
D. Eighty

Answer 1

Hint: The product of HCF and LCM of two given numbers is the same as the product of two given numbers, here the first number is $280$ consider the other number be $x$.

Complete step-by-step answer:
Given that
LCM of two numbers is fourteen times HCF
Therefore we can write ${\text{LCM = 14HCF}}$
Also given that sum of HCF and LCM $ = 600$
Hence equation is:
$
  {\text{14HCF + HCF = 600}} \\
  {\text{15HCF = 600}} \\
  \therefore {\text{HCF = 40}} \\
$
Therefore LCM $ = 600 - 40 = 560$
Now it's given that one number is $280$
Let the other number be $x$
Since LCM multiplied by HCF is equals to product of both numbers, therefore equation is:
$
   \Rightarrow 560 \times 40 = 280 \times x \\
   \Rightarrow x = \dfrac{{560 \times 40}}{{280}} \\
   \Rightarrow x = 2 \times 40 \\
   \Rightarrow x = 80 \\
$
Therefore the other number is $80$.
Hence the correct option is D.

Note: In this question it's given that LCM of two numbers is fourteen times their HCF so from this we took ${\text{LCM = 14HCF}}$also its given that their sum is $600$ so from this we calculated that LCM is $560$ now one number is given and we took other number as $x$ and since LCM multiplied by HCF is equals to product of both numbers hence we calculated that other number is eighty.