Question

If the A.M. between two numbers exceeds their G.M. by 12 and the G.M. exceeds their H.M. by 36/5, then the greater of the two numbers is .

• A. 72
• B. 54
• C. 18
• D. 48

Answer 1

The correct option is B 54

Let the A.M., G.M., and H.M. of the two numbers a and b (a > b) be represented by A, G, and H respectively.
A-G=12 and G-H=36/5
$G^2=AH=\left(G+12\right)\left(G-\frac{36}{5}\right)\Rightarrow G^2=G^2-\frac{36G}{5}+12G-\frac{432}{5}\Rightarrow \frac{36G}{5}-12G=-\frac{432}{5}\Rightarrow -\frac{24G}{5}=-\frac{432}{5}\Rightarrow G=18\therefore A=30\Rightarrow a+b=60G=18\Rightarrow \sqrt{ab}=18\Rightarrow ab=324\therefore a=54andb=6asa>b$