| If 30% of \[(B-A)\]is equal to 18% of \[(B+A),\] then the ratio of A : B is equal to |
A) 4 : 1
B) 1 : 4
C) 6 : 4
D) 5 : 9
Correct Answer: B
Solution :
| Given, 30% of \[(B-A)=18%\,\,(A+B)\] |
| \[\Rightarrow \]\[(B-A)\times \frac{30}{100}=(A+B)\times \frac{18}{100}\] |
| \[\Rightarrow \]\[\frac{B-A}{B+A}=\frac{18}{30}=\frac{9}{15}=\frac{3}{5}\] |
| By componendo and dividendo |
| If \[\frac{a}{b}=\frac{c}{d},\]then \[\frac{a+b}{a-b}=\frac{c+d}{c-d}\] |
| \[\Rightarrow \] \[\frac{2B}{-\,\,2A}=\frac{3+5}{3-5}=\frac{8}{-2}\] |
| \[\Rightarrow \] \[\frac{B}{A}=\frac{4}{1}\] |
| \[\therefore \] \[\frac{A}{B}=\frac{1}{4}\] |
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