Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
There are two concentric circles $C_{2}$ and $C_{2}$ with radii $r_{1}$ and $r_{2}$. The circles are such that $C_{1}$ fully encloses $C_{1}$. Then, what is the radius of $\mathrm{C}_{1}$ ?
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
I. $2 \pi\left(r_{1}-r_{2}\right)=k \Rightarrow r_{1}-r_{2}=\frac{k}{2 \pi}$ II. $\pi\left(r_{1}^{2}-r_{2}^{2}\right)=m \Rightarrow\left(r_{1}^{2}-r_{2}^{2}\right)=\frac{m}{\pi} \Rightarrow\left(r_{1}-r_{2}\right)\left(r_{1}+r_{2}\right)=\frac{m}{\pi}$ $\Rightarrow\left(r_{1}+r_{2}\right)=\frac{m}{\pi} \times \frac{2 \pi}{k}=\frac{2 m}{k}$ Adding (i) and (ii) we get : $2 r_{1}=\frac{k}{2 \pi}+\frac{2 m}{k}=\frac{k^{2}+4 m \pi}{2 k \pi}$ $\Rightarrow r_{1}=\frac{k^{2}+4 m \pi}{4 k \pi}$. Thus, both I and II together give the answer. ∴ Correct answer is (e).
Explanation as extracted from the printed page; notation may be imperfect.