Question

यदि \( \sqrt{ p }-\sqrt{ q }=20 \) है, तब \( \left(\frac{ p -5 q }{100}\right) \) का अधिकतम मान है: 

(A) 5 (B) 10 (C) 15 (D) 25

Answer 1

Correct option is (A) 5

\(\sqrt{p}-\sqrt{q}=20\)

\(\therefore\,\sqrt{p}=20+\sqrt{q}\) .......(1)

5q² both sides

\((\sqrt{p})^2=(20+\sqrt{q})^2\)

P = 400 + q + \(40\sqrt{q}\)

Putting the value of 'P' in eq.

⇒ \(\frac{P-5q}{100}\)

⇒ \(\frac{400+q+40\sqrt{q}-5q}{100}\)

⇒ \(\frac{400+40\sqrt{q}-4q}{100}\)

f(q) \(=\frac{400+40\sqrt{q}-4q}{100}\)

Differentiating both sides w.r to q

\(f'(q)=0+\frac{40}{2\sqrt{q}}-4\)

\(f'(q)=\frac{20}{\sqrt{9}}-4\)

\(f'(q)=0\)

\(\frac{20}{\sqrt{q}}-4=0\)

\(\frac{20}{\sqrt{q}}=4\)

\(\sqrt{q}=5\)

q = 25

Now, Putting the value of p & q in f(q)

f(q) = \(\frac{400+40\times 5-20}{100}=5\)