Quantitative Aptitude Ques 2308

Question: If 5 tan A = 4, then the value of $ \frac{5\sin A-3\cos A}{\sin A+2,\cos A} $ is

Options:

A) $ \frac{9}{14} $

B) $ \frac{5}{6} $

C) $ \frac{7}{9} $

D) $ \frac{5}{14} $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ 5\tan A=4 $
    $ \Rightarrow $ $ \tan A=\frac{4}{5} $

$ \therefore $ $ AC=\sqrt{16+25}=\sqrt{41} $ Now, $ \frac{5\sin A-3\cos A}{\sin A+2\cos A} $ $ =\frac{5\times \frac{4}{\sqrt{41}}-3\times \frac{5}{\sqrt{41}}}{\frac{4}{\sqrt{41}}+2\times \frac{5}{\sqrt{41}}}=\frac{20-15}{4+10}=\frac{5}{14} $

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