Question

The l.C.M of two numbers is 495 and their h.C.F is 5. If the sum of the numbers is 100, then their difference is a) 10 b) 46 c) 70 d) 90

Answer 1

L.C.M=495
H.C.F=5
a*b=5*495=2475
a+b=100___(1)
a=100-b
(100-b)b=2475
100b-b^2=2475
b^2-100b+2475=0
b^2-45b-55b+2475=0
b(b-45)-55(b-45)=0
b=55,45
put b=55,45 in __(1)
if b=55
a=100-55
=45
if b=45
a=100-45
=55