SATHEE: Quantitative Aptitude Ques 1888

Quantitative Aptitude Ques 1888

Question: If $ \frac{\frac{1}{\sqrt{9}}-\frac{1}{\sqrt{11}}}{\frac{1}{\sqrt{9}}+\frac{1}{\sqrt{11}}}\times \frac{10+\sqrt{99}}{x}=\frac{1}{2}, $ then the value of $ x $ is

Options:

A) 2

B) 3

C) 4

D) 5

Show Answer

Answer:

Correct Answer: A

Solution:

$ \frac{\frac{1}{\sqrt{9}}-\frac{1}{\sqrt{11}}}{\frac{1}{\sqrt{9}}+\frac{1}{\sqrt{11}}}=\frac{\sqrt{11}-\sqrt{9}}{\sqrt{11}+\sqrt{9}}=\frac{\sqrt{11}-\sqrt{9}}{\sqrt{11}+\sqrt{9}}\times \frac{\sqrt{11}-\sqrt{9}}{\sqrt{11}-\sqrt{9}} $ $ =\frac{11+9-2\sqrt{99}}{11-9}=\frac{2(10-\sqrt{99})}{2}=10-\sqrt{99} $

$ \therefore $ $ \frac{(10-\sqrt{99})\times (10+\sqrt{99})}{x}=\frac{1}{2} $
$ \Rightarrow $ $ \frac{100-99}{x}=\frac{1}{2} $

$ \Rightarrow $ $ \frac{1}{x}=\frac{1}{2} $
$ \Rightarrow $ $ x=2 $

Quantitative Aptitude Ques 1887

Quantitative Aptitude Ques 1889

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