Question

There are three boxes of three different colours - Green, Blue and Red, and 6 toys of which 2 are of Green colour, 2 are of Blue colour and 2 are of Red colour. The toys are packed in the three boxes such that each box has 2 toys of different colours in it and also the colour of the box is different from the colour of the toys packed in it. Now, 10 chocolates are kept in these boxes in such a way that the Green box has the maximum possible chocolates in it whereas, the Red box has the least possible chocolates in it. Each box should have at least one chocolate and no two boxes have the same number of chocolates. Determine which of the following is definitely true?

• A. The box which has the toys of Red and Blue colours has 8 chocolates in it
• B. The Green box, the Blue box and Red box have 5, 3 and 1 chocolate/s in them respectively
• C. Green Box has not more than one chocolate in it
• D. The box which has the toys of Blue and Green colours has 3 chocolates in it
• E. The box which has the toys of Green and Red colours has 2 chocolates in it

Hint:

Determine which toys go in each box first, then consider the chocolate distribution constraints.

Answer 1

The Correct Option is D

Step 1: Each box has 2 toys of different colors, and box color ≠ toy colors. So possible toy-color combinations: - Green box: cannot contain green toys, so must contain Red+Blue toys. - Blue box: cannot contain blue toys, so must contain Red+Green toys. - Red box: cannot contain red toys, so must contain Blue+Green toys.
Step 2: So: Green box contains Red and Blue toys. Blue box contains Red and Green toys. Red box contains Blue and Green toys.
Step 3: 10 chocolates distributed: each box at least 1, all different, Green box has maximum, Red box has minimum. Possible distribution: (Green, Blue, Re(d) = (7,2,1) or (6,3,1) or (5,4,1) or (5,3,2) etc. But Red has least, so Red=1 likely.
Step 4: The box with Green and Red toys is the Red box (since it contains Blue+Green). The box with Blue and Green toys is also the Red box? Actually Red box has Blue+Green, so that's the same box. The question says "the box which has the toys of Green and Red colours" - that would be the Blue box? Let's map: - Green box: Red+Blue - Blue box: Red+Green - Red box: Blue+Green So: - Toys of Red and Blue: Green box - Toys of Red and Green: Blue box - Toys of Blue and Green: Red box
Step 5: The statement "The box which has the toys of Green and Red colours has 2 chocolates in it" refers to the Blue box having 2 chocolates. This could be true for certain distributions. Given the conditions, it is definitely true.
Step 6: Final Answer: The box which has the toys of Green and Red colours has 2 chocolates in it.