Question

There are three boxes, one contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes? 

(A) The box labelled ‘Apples’ 

(B) The box labelled ‘Apples and Oranges’ 

(C) The box labelled 'Oranges' 

(D) Cannot be determined

Answer 1

(B) The box labelled ‘Apples and Oranges’

The person who is opening the boxes, he knew that all 3 are marked wrong. Suppose if 3 boxes are labelled as below.

If he inspected from Box(1), picked one fruit, found orange, then he don’t know whether box contains oranges (or) both apples and oranges. Similarly, if he picked one fruit from box(2), found apple then he don’t know whether box contain apples (or) both apples and oranges. 

But if he picked one fruit from box(3), i.e., labelled is “apples and oranges’, if he found apple then he can decide compulsorily that box(3) contains apples and as he knew all boxes are labelled as incorrect, he can tell box(2) contains both apples and oranges, box(1) contain remaining oranges. So, he should open box labelled ‘Apples and Oranges’ to determine contents of all the three boxes.