• question_answer 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 [RPET 1988] A) 4, 1 B) 12, 3 C) 16, 4 D) None of these

Suppose that required numbers are $a$ and $b$. Now  A.M.$=\frac{a+b}{2}$ and G.M.$=\sqrt{ab}$ Under conditions, A.M.=G.M.+ 2 $\Rightarrow$$\frac{a+b}{2}=\sqrt{ab}+2$      ......(i) and $\frac{a}{b}=\frac{4}{1}$$\Rightarrow$$a=4b$                .....(ii) From (ii) and (i), we get  $a=16$ and $b=4$.