Question

If the A.M. of two numbers is greater than G.M. of the numbers by 2 and the ratio of the numbers is 4 : 1, then the numbers are

• A. 4, 1
• B. 12, 3
• C. 16, 4
• D. None of these

Answer 1

Answer: (C)

16, 4

Answer 2

Let x and y be the numbers

∴ A.M. = G.M. + 2 ⇒ $\frac { x + y } { 2 } = \sqrt { x y } + 2$

Also, $\frac { x } { y } = 4 : 1$ ⇒ $x = 4 y$

∴ $\frac { 5 y } { 2 } = 2 y + 2$ ⇒ $y = 4$

⇒ $x = 4 \times 4 = 16$

∴ The numbers are 16, 4.