Two positive numbers are in the ratio of 3 : 4 and the product of their LCM and HCF is 1200. The sum of the numbers is:

Correct option is A

Given:
Ratio of Two numbers = 3 : 4
HCF × LCM = 1200
Formula used:
Product of two numbers = Product of their HCF and LCM
Solution:
Let the numbers be 3x, 4x respectively
HCF of 3x and 4x = x
LCM = 3 × 4 × x = 12x
Now, HCF × LCM = 1200
=> x × 12x = 1200
=> 12x$$^2$$​​ = 1200
=> x$$^2$$​ = 100
=> x = 10
Sum of numbers = 3x + 4x = 7x = 7 × 10
= 70