Q237 / 270 · NDA 2021 (Phase 1) · Mathematics

If $x+y=20$ and $P=x y$, then what is the maximum value of $P$ ?

  • Correct answer
    A
    $100$
  • B
    $96$
  • C
    $84$
  • D
    $50$

Solution

$x+y=20 \text { and } P=x y$ A.M. of $x$ and $y=\frac{x+y}{2}=\frac{20}{2}=10$. G.M. of $x$ and $y=\sqrt{x \cdot y}=\sqrt{P}$ As, A.M. $\geq$ G.M. $\therefore 10 \geq \sqrt{P}$ Hence, $P_{\max .}=(10)^2=100$.

Hence, the correct answer is option: 'A'.

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