Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
Two numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers be in the ratio of $3: 4$, the numbers are
(a)6, 8
(b)9, 12
(c)12, 16
(d)None of these
Answer
Answer (as printed): A
Explanation
Let the numbers be $3 x$ and $4 x$. Then, $(4 x)^{2}=8 \times(3 x)^{2}-224$ $$\begin{aligned} & \Leftrightarrow 16 x^{2}=72 x^{2}-224 \\ & \Leftrightarrow 56 x^{2}=224 \Leftrightarrow x^{2}=4 \\ & \Leftrightarrow x=2 . \end{aligned}$$ So, the numbers are 6 and 8.
Explanation as extracted from the printed page; notation may be imperfect.