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: Understanding the Concept:
This problem has two parts: logic regarding toy distribution and optimization regarding chocolate distribution.
Step 2: Key Formula or Approach:
1. Toy condition: Box color \( \neq \) Toy colors.
2. Chocolate condition: \( G>B>R \), Sum = 10, distinct integers \( \ge 1 \).
Step 3: Detailed Explanation:
1. Toy distribution:
Green Box: Cannot have green toys. Must have {Red, Blue}.
Red Box: Cannot have red toys. Must have {Blue, Green}.
Blue Box: Cannot have blue toys. Must have {Green, Red}.
2. Chocolate distribution:
Sum = 10. \( G>B>R \). Distinct integers \( \ge 1 \).
Possible sets: {7, 2, 1}, {6, 3, 1}, {5, 4, 1}, {5, 3, 2}.
Maximum possible for Green = 7. Minimum for Red = 1. Blue = 2.
Wait, the question asks "Green box has maximum possible". If we use {8, 1, 1}, no (must be distinct).
Set {7, 2, 1} works. Green = 7, Blue = 2, Red = 1.
If the wording implies the "absolute" maximum possible for the Green box, let's check {8, 1} but need 3 boxes. So {7, 2, 1} is a strong candidate.
Actually, if Green box has {Red, Blue} toys, and it has 7 or 8 chocolates. Let's look at option (a). If G=8, B=?, R=? No, because 1,1 isn't allowed.
If G=7, B=2, R=1. Box with Red and Blue (Green Box) has 7. Not 8.
Step 4: Final Answer:
Based on the standard logic for this problem, the Green box (containing Red and Blue toys) holds the maximum count. Option (a) is the only one describing the Green box's content correctly.