# Find two numbers whose arithmetic mean is 12.5 and geometric mean is 10.

(a) 20, 4

(b) 15, 10

(c) 20, 5

(d) None of these

**Answer: (c) 20, 5 **

**Solution:-**

Let the two numbers be X and Y.

The arithmetic mean of two numbers is 12.5 and geometric mean is 10.

Then, (X + Y)/2 = 12.5 & sqrt.(X Y) = 10

X + Y = 12.5 x 2 & X Y = 100

X + Y = 25 & X Y = 100

X = 25 – Y …………… (1)

Then, (Y – 25) Y = 100

Y^2 – 25 Y = 100

Y^2 – 25 Y – 100 = 0

Y^2 – 20 Y – 5 Y – 100 = 0

Y (Y – 20) – 5 (Y – 20) = 0

(Y – 5) (Y – 20) = 0

Y – 5 = 0 & Y – 20 = 0

Y = 5 & Y = 20

Put the value of Y in equation (1),

Then, X = 25 – 5 = 20.

Then, the two numbers are 20 and 5.

Hence, the correct answer is option (c) 20, 5.