Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of

Question

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.

Options:

A . 2 : 3

B . 1 : 1

C . 3 : 4

D . 4 : 3

Answer: Option D

5% of A + 4% of B = (6% of A + 8% of B)\(\frac{2}{3}\)

= \(\frac{5}{100}A + \frac{5}{100}B = \frac{2}{3}\left(\frac{6}{100}A + \frac{8}{100}B\right)\)

= \(\frac{1}{100}A +\frac{1}{100}B =\frac{1}{25}A + \frac{1}{75}B\)

= \(\left(\frac{1}{20}-\frac{1}{25}\right)A =\left(\frac{4}{75}- \frac{1}{25}\right)B\)

= \(\frac{1}{100}A =\frac{1}{75}B\)

\(\frac{A}{B} =\frac{100}{75}=\frac{4}{3 }.\)

So, Required ratio = 4:3.

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