| Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. The ratio A : B is [NICL (AO) 2015] |
A) 1 : 1
B) 2 : 3
C) 3 : 2
D) 3 : 4
E) 4: 3
Correct Answer: E
Solution :
| According to the question, |
| \[\frac{A\times 5}{100}+\frac{B\times 4}{100}=\frac{2}{3}\left( \frac{A\times 6}{100}+\frac{B\times 8}{100} \right)\] |
| \[\Rightarrow \] \[\frac{5A}{100}+\frac{4B}{100}=\frac{2}{3}\left( \frac{6A}{100}+\frac{8B}{100} \right)\] |
| \[\Rightarrow \] \[\frac{5A+4B}{100}=\frac{2}{3}\left( \frac{6A+8B}{100} \right)\] |
| \[\Rightarrow \] \[15A+12B=12A+16B\] |
| \[\Rightarrow \] \[3A=4B\,\,\frac{A}{B}=\frac{4}{3}\] |
| \[\therefore \] \[A:B=4:3\] |
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