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.

Given Relation

• 0.05A + 0.04B equals two-thirds of (0.06A + 0.08B)

Write the Equation
0.05A + 0.04B = (2/3) × (0.06A + 0.08B)0.05A + 0.04B = 0.04A + 0.053333…B

Collect Like Terms
(0.05 − 0.04)A = (0.053333… − 0.04)B0.01A = 0.013333…BA/B = 0.013333… ÷ 0.01 = 1.3333… = 4/3

Alternative Fractional Method
Multiply all terms by 300 to clear decimals:15A + 12B = (2/3) × (18A + 24B) ⇒ 15A + 12B = 12A + 16B3A = 4B ⇒ A:B = 4:3

Final Answer
A:B = 4:3.