The ratio of two numbers is 3 : 5 and their LCM is 42 greater than their HCF. What is the value of the larger number?

Correct option is C

Given:
Ratio of two numbers = 3 : 5
LCM = 42 + HCF
Formula Used:
(i) If a and b are two numbers, then a × b = HCF × LCM
(ii) HCF of two numbers is the highest common factor of both of them.
Solution:
Let the numbers be 3x and 5x.
Then, H.C.F. = x
a × b = HCF × LCM
=> 3x × 5x = x × (42 + x)
=> 15x = 42 + x
=> 14x = 42
=> x = 3
Larger number = 5x = 5 × 3= 15
∴ The value of the larger number is 15.