Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
If the sum of two numbers is 10 and the sum of their reciprocals is $\frac{5}{12}$, find the numbers. (P.C.S., 2006)
Answer
Answer (as printed):
Explanation
Let the numbers be $x$ and $y$. Then, $x+y=10$ ...(i) And, $\frac{1}{x}+\frac{1}{y}=\frac{5}{12} \Rightarrow \frac{x+y}{xy}=\frac{5}{12} \Rightarrow xy=\frac{10\times12}{5}=24$ ...(ii) $\therefore x-y=\sqrt{(x+y)^{2}-4xy}=\sqrt{(10)^{2}-4\times24}=\sqrt{100-96}=\sqrt{4}=2 \Rightarrow x-y=2$ ...(iii) Adding (i) and (iii), we get: $2x=12$ or $x=6$. Putting $x=6$ in (i), we get: $y=4$. Hence, the required numbers are 6 and 4.
Explanation as extracted from the printed page; notation may be imperfect.