Question # The LCM of two numbers is 4 times their HCF. The sum of LCM and ( mathrm{HCF} ) is ( 125 . ) If one of the number is 100 , then the other number is ( quad ) RRB NTPC (Phase I) 2016

# The LCM of two numbers is 4 times their HCF. The sum of LCM and ( mathrm{HCF} ) is ( 125 . ) If one of the number is 100 , then the other number is ( quad ) RRB NTPC (Phase I) 2016

(1) 5

(2) 25

(3) 100

(4) 125

Solution

(2) Let ( quad H C F=x )

( therefore quad L C M=4 x ) ( Rightarrow quad x+4 x=125 )

( Rightarrow quad x=frac{125}{5}=25 )

( therefore mathrm{HCF}=25, mathrm{LCM}=4 times 25=100 ) and one number ( =100 )

Hence, second number ( =frac{H C F times L C M}{text { One number }} )

( =frac{25 times 100}{100}=25 )