Change their numerator to the same first.

1/5 = 2/10

Based on the fraction,

The first case : 2 apples eaten, no oranges eaten.

After eating 2 apples, we can take it as there are 10 units of fruits left.

Total Apples at first = 2 units + 2
Oranges at first = 8 units (since not eaten here)


Second case : 1 orange eaten, no apples eaten.


2/7 of fruits left are apples, and it's just the original number of apples since no apples are eaten.

This tells us that:
2/7 of fruits left = 2 units + 2

1/7 of fruits left
= (2 units + 2) ÷ 2
= 1 unit + 1

1 - 2/7 = 5/7
5/7 of fruits left are oranges.

5/7 of fruits = 5 x (1 unit + 1)
= 5 units + 5


Add back 1 orange such that we have the original number of oranges.

5 units + 5 + 1 = 5 units + 6

Now this is equal to 8 units in the first case since no oranges were eaten for that case.


5 units + 6 = 8 units

8 - 5 = 3

To get to 8 units from 5 units,, we add 6 fruits. That's the same as adding 3 units

So 3 units = 6

1 unit = 6 ÷ 3 = 2


So ,


Oranges in the basket
= 8 units
= 8 x 2
= 16

Apples
= 2 units + 2
= 2 x 2 + 2
= 4 + 2
= 6