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. Find the ratio of A : B.
2 : 3
1 : 1
3 : 4
4 : 3
Explanation:
p>5% of A + 4% of B =$ \dfrac{2}{3} $ (6% of A + 8% of B)
p>5% of A + 4% of B =$ \dfrac{2}{3} $ (6% of A + 8% of B)
$\Rightarrow \dfrac{5}{100} $ A +$ \dfrac{4}{100} $ B=$ \dfrac{2}{3} \left(\dfrac{6}{100} A +\dfrac{8}{100} B\right) $
$\Rightarrow \dfrac{1}{20} $ A +$ \dfrac{1}{25} $ B=$ \dfrac{1}{25} $ A +$ \dfrac{4}{75} $ B
$\Rightarrow \left(\dfrac{1}{20} -\dfrac{1}{25} \right) $ A = $ \left(\dfrac{4}{75} -\dfrac{1}{25} \right) $ B
$\Rightarrow \dfrac{1}{100} $ A =$ \dfrac{1}{75} $ B
$ \dfrac{A}{B} $=$ \dfrac{100}{75} $=$ \dfrac{4}{3} $.
$\therefore$ Required ratio = 4 : 3