Question

the ratio of two numbers is 2/3. if 2 is subtracted from the first and 8 from the second, the ratio bevomes the reciprocal of the original ratio. find the numbers by simultaneous method.

Answer 1

Let the fraction be 2x/3x.

$\frac{2x - 2}{3x - 8} = \frac{3}{2} \\ \\ \\ 2(2x - 2) = 3(3x - 8) \\ \\ = 4x - 4 = 9x - 24 \\ \\ 9x - 4x = 24 - 4 \\ \\ = 5x = 20 \\ \\ x = \frac{20}{5} = 4 \\ \\ \\ 2x = 2 \times 4 = 8 \\ \\ 3x = 3 \times 4 = 12$

∴ The numbers are 8 and 12.

And the fraction is 8/12.

$\frac{8}{12} = \frac{2}{3} \\ \\ \frac{8 - 2}{12 - 8} = \frac{6}{4} = \frac{3}{2}$

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