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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 120
H.C.F = L.C.M/20
H.C.F/L.C.M = 1/20 = 1 : 20
Let the common ratio be x.
L.C.M - H.C.F = 456
20x - x = 456
19x = 456
x = 25
H.C.F = 24
L.C.M = 20(24) = 480
One number = 96
Let the other number be y.
L.C.M(H.C.F) = Product of two numbers
480(24) = 96y
y = 11520/96 = 120