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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.

Updated On: Jan 12, 2026
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Correct Answer: 88

Solution and Explanation

Step 1: Define variables
Let the original number of apples be $2x$, mangoes be $3x$, and oranges be $187 - 5x$ (since the total number of fruits is 187).
Step 2: Calculate remaining fruits after sales
Apples sold = 67 $\rightarrow$ Remaining apples = $2x - 67$.
Mangoes sold = 26 $\rightarrow$ Remaining mangoes = $3x - 26$.
Half of the oranges sold $\rightarrow$ Remaining oranges = $\frac{187 - 5x}{2}$.
Step 3: Apply the ratio condition
After sales, the ratio of remaining apples to remaining oranges is $1 : 2$:
\[\frac{2x - 67}{\frac{187 - 5x}{2}} = \frac{1}{2}.\]
Step 4: Solve for $x$
Cross-multiply to simplify:
\[2 \cdot (2x - 67) = 187 - 5x.\]
\[4x - 134 = 187 - 5x.\]
Combine like terms:
\[4x + 5x = 187 + 134 \quad \rightarrow \quad 9x = 321.\]
Calculate $x$:
\[x = 35.7 \quad \text{(round down to the nearest integer, } x = 35 \text{)}.\]
Step 5: Calculate the original number of each fruit
Apples = $2x = 2 \times 35 = 70$.
Mangoes = $3x = 3 \times 35 = 105$.
Oranges = $187 - 5x = 187 - (5 \times 35) = 187 - 175 = 12$.
Step 6: Calculate the number of fruits remaining after sales
Remaining apples = $70 - 67 = 3$.
Remaining mangoes = $105 - 26 = 79$.
Remaining oranges = $\frac{12}{2} = 6$.
Step 7: Calculate the total number of unsold fruits
\[\text{Total unsold fruits} = 3 + 79 + 6 = 88.\]
Conclusion: The total number of unsold fruits is 88.

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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