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} $
BETA
