• question_answer Two numbers are such as that square of one is 224 less than 8 times the square of the other. If the numbers are in the ratio of 3 : 4, they are: A) 12, 16              B)          6, 8 C) 9, 12                D)          None of these

Given, ratio of numbers is 3 : 4 $\therefore$    The numbers are 3x and 4x. Now, according to the question $16{{x}^{2}}=8{{(3x)}^{2}}\,-224$ $\Rightarrow$            $16{{x}^{2}}=72{{x}^{2}}\,-224$ $\Rightarrow$            $56{{x}^{2}}=224$ $\Rightarrow$            $x=2$ $\therefore$    Required numbers = 6, 8