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.

Answer 1

Let the original number of oranges and apples be 7x and 13x.

According to the given information,

`(7x - 8)/(13x - 11) = 1/2`

`\implies` 2(7x – 8) = 1(13x – 11)

`\implies` 14x – 16 = 13x – 11

`\implies` 14x – 13x = –11 + 16

`\implies` x = 5

Thus, the original number of oranges and apples are  7 × 5 = 35 and  13 × 5 = 65 respectively.