If one number is 80\% of the other and 4 times the sum of their squares is 656, then the numbers are
(a)4, 5
(b)8, 10
(c)16, 20
(d)None of these
Answer
Answer (as printed): B
Explanation
Let one number $=x$. Then, other number $=80 \%$ of $x=\frac{4 x}{5}$. $$\begin{array}{r} \therefore 4\left[x^{2}+\left(\frac{4}{5} x\right)^{2}\right]=656 \Leftrightarrow x^{2}+\frac{16}{25} x^{2}=164 \Leftrightarrow \frac{41}{25} x^{2}=164 \\ \Leftrightarrow x^{2}=\left(\frac{164 \times 25}{41}\right)=100 \Leftrightarrow x=10 . \end{array}$$ So, the numbers are 10 and 8.
Explanation as extracted from the printed page; notation may be imperfect.