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Question

In a basket, the ratio between the number of oranges and the number of apples is 7 : 13. If 8 oranges and 11 apples are eaten, the ratio between the number of oranges and the number of apples becomes 1 : 2. Find the original number of oranges and the original number of apples in the basket.

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Solution

Let the original number of oranges and apples be 7x and 13x.
According to the given information,
fraction numerator 7 x minus 8 over denominator 13 x minus 11 end fraction equals 1 half 14 x minus 16 equals 13 x minus 11 x equals 5
Thus, the original number of oranges and apples are 7 × 5 = 35 and 13 × 5 = 65 respectively.

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