The HCF of two numbers is one-twentieth of their LCM. If one of the numbers is 96 and the difference of the LCM and the HCF is 456 then what is the other number?

Correct option is B

Concept Used:
LCM × HCF = Product of the two numbers
Solution:
According to the question,
HCF = $$\frac1{20}$$​ × LCM …(i)
LCM - HCF = 456
=> LCM - ($$\frac{1}{20}$$​ × LCM) = 456
=>$$\frac{19}{20}$$​ × LCM = 456
=> LCM = $$\frac {(456 × 20)}{19}$$​​
=> LCM = 480
Then HCF = (480 - 456) = 24
Let the other number be y
y × 96 = 24 × 480
=> y = $$\frac{11520}{96}$$​​
=> y = 120