For two positive real number's a and b, If the A.M. exceeds their G.M. by 2 and the G.M. exceeds their H.M. by 85, then the value of a+b is
A
20
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
30
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
40
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
50
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A20 Let the A.M., G.M. and H.M. be A,G and H respectively, A−G=2⋯(1) G−H=85⋯(2)
We know that, G2=AH
Using equation (1) and (2), ⇒G2=(G+2)(G−85)⇒G2=G2+(2−85)G−165⇒2G5=165⇒G=8
Now, A=a+b2=2+G∴a+b=20