A ate grapes and pineapple; B ate grapes and oranges; C ate oranges, pineapple and apple; D ate grapes, apple and pineapple. After taking fruits, B and C fell sick. In the light of the above facts, it can be said that the cause of sickness was:

The correct option is Oranges.

To determine the cause of sickness, we can analyze the common fruit consumed by only the individuals who fell sick (B and C). Let's list the fruits eaten by each person:
- A ate grapes and pineapple.
- B ate grapes and oranges.
- C ate oranges, pineapple, and apple.
- D ate grapes, apple, and pineapple.

According to the given facts, only B and C fell sick. Therefore, the cause of the sickness must be a fruit that both B and C ate, and that the healthy individuals (A and D) did not eat.

Let's check the fruits eaten by B and C:
- B ate: {grapes, oranges}
- C ate: {oranges, pineapple, apple}

The common fruit eaten by both B and C is oranges.

To confirm, we check if any healthy individuals ate oranges:
- A did not eat oranges (ate grapes and pineapple).
- D did not eat oranges (ate grapes, apple, and pineapple).

Since oranges were eaten only by the individuals who fell sick (B and C) and not by anyone who remained healthy (A and D), it can be concluded that the cause of sickness was oranges.