If $1.5x = 0.04y$, then the value of $\dfrac{y-x}{y+x}$ is:

Question

There are 187 fruits in total. The ratio of apples to mangoes is $2 : 3$, and the rest are oranges. After selling 67 apples, 26 mangoes, and half of the oranges, the ratio of the remaining apples to oranges becomes $1 : 2$. Determine how many unsold fruits remain.

Answer 1

Divide both sides of $1.5x = 0.04y$ by $y$ to get $\dfrac{x}{y} = \dfrac{0.04}{1.5} = \dfrac{2}{75}$.
Write the target expression in terms of this single ratio by dividing numerator and denominator of $\dfrac{y-x}{y+x}$ by $y$: $\dfrac{1 - x/y}{1 + x/y}$.
Substitute $x/y = 2/75$: $\dfrac{1 - 2/75}{1 + 2/75} = \dfrac{73/75}{77/75} = \dfrac{73}{77}$.
\[\boxed{\dfrac{73}{77}}\]

If \(1.5x = 0.04y\), then the value of \(\dfrac{y-x}{y+x}\) is:

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The Correct Option is A

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