Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2006 · Marks: · Difficulty:
The sum of two numbers is 15 and the sum of their squares is 113. Find the numbers.
Answer
Answer (as printed):
Explanation
Let the numbers be $x$ and $(15-x)$. Then, $x^{2}+(15-x)^{2}=113 \Rightarrow x^{2}+225+x^{2}-30x=113 \Rightarrow 2x^{2}-30x+112=0 \Rightarrow x^{2}-15x+56=0 \Rightarrow (x-7)(x-8)=0 \Rightarrow x=7 \text{ or } x=8$. So, the numbers are 7 and 8.
Explanation as extracted from the printed page; notation may be imperfect.