Discussion
12.5% of a positive number is 62.5% of the other positive number. If the sum of squares of both numbers is 416, smallest number is what percentage of sum of both the numbers ?
Answer: D
The smaller number is \(16\frac{2}{3}\)% of the sum.
Let the numbers be x and y. Since 12.5% of x equals 62.5% of y, x = 5y. Then use the sum of squares:
\[ \begin{aligned} (5y)^{2} + y^{2} &= 416 \\ 26y^{2} &= 416 \\ y^{2} = 16, \ y &= 4, \ x = 20 \end{aligned} \]
The smaller number is 4 and the sum is 24:
\[ \frac{4}{24} \times 100 = 16\tfrac{2}{3}\% \]
\(83\frac{1}{3}\)% is the larger number's share (20 out of 24), and 20% and 25% compare the smaller number with the larger (4/20) or use a wrong ratio, not with the sum.
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