COMEDK 2024 Shift 2 Paper

Let the two positive numbers be a and b such that their ratio is:
‌

a

b

=‌

3+2√2

3−2√2

To find the arithmetic mean (A.M) of a and b, we use the formula:
A.M =‌

a+b

2

The geometric mean (G.M) of a and b is given by:
‌ G.M ‌=√ab
Let's assume a=k(3+2√2) and b=k(3−2√2), where k is a positive constant. This makes the ratio correct. Now, compute the A.M and G.M:
Next, find the G.M:
Notice that
(3+2√2)(3−2√2)=32−(2√2)2=9−8=1
Hence, G.M becomes:
G.M=k√1=k
Now, the ratio between their A.M and G.M is:
‌

‌ A.M ‌

‌ G.M ‌

=‌

3k

k

=3
Therefore, the ratio is 3:1.
The correct answer is Option D:
Option D
3:1