Ashutosh has six bags full of blue and white balls which he wishes to sell. Bag 1 has 29 balls, bag 2 has 14 balls, bag 3 has 23 balls, bag 4 has 6 balls, bag 5 has 5 balls and bag 6 has 12 balls. Ashutosh now tells his friends : "If I sell all the balls of a particular bag, I will have twice as many blue balls left as white balls. "If we know that a bag contains balls of only one colour, can you tell the bag he was talking about?

Options

A. bag 1
B. bag 2
C. bag 4
D. bag 5

Answer

To solve the problem, we need to analyze the information given about the bags and the condition that Ashutosh mentioned regarding the number of blue and white balls left after selling all the balls from one bag.

### Step-by-Step Solution:

1. **Identify the Total Number of Balls in Each Bag:**
- Bag 1: 29 balls
- Bag 2: 14 balls
- Bag 3: 23 balls
- Bag 4: 6 balls
- Bag 5: 5 balls
- Bag 6: 12 balls

2. **Understand the Condition:**
- Ashutosh states that if he sells all the balls from a particular bag, he will have twice as many blue balls left as white balls.

3. **Formulate the Problem:**
- Let’s denote:
- \( B \) = number of blue balls left
- \( W \) = number of white balls left
- According to the condition, after selling all the balls from one bag, the relationship is:
\[ B = 2W \]

4. **Evaluate Each Bag:**
- We will check each bag to see if selling it results in the condition \( B = 2W \) being satisfied.

- **If Bag 1 (29 balls) is sold:**
- Remaining balls = Total balls - 29
- \( B + W = 29 \) (not possible since we need to check the condition)

- **If Bag 2 (14 balls) is sold:**
- Remaining balls = Total balls - 14
- \( B + W = 14 \) (not possible since we need to check the condition)

- **If Bag 3 (23 balls) is sold:**
- Remaining balls = Total balls - 23
- \( B + W = 23 \) (not possible since we need to check the condition)

- **If Bag 4 (6 balls) is sold:**
- Remaining balls = Total balls - 6
- \( B + W = 6 \)
- Let’s say \( W = x \), then \( B = 2x \)
- So, \( 2x + x = 6 \) → \( 3x = 6 \) → \( x = 2 \)
- Thus, \( W = 2 \) and \( B = 4 \)
- This satisfies \( B = 2W \) (4 = 2 * 2).

- **If Bag 5 (5 balls) is sold:**
- Remaining balls = Total balls - 5
- \( B + W = 5 \) (not possible since we need to check the condition)

- **If Bag 6 (12 balls) is sold:**
- Remaining balls = Total balls - 12
- \( B + W = 12 \) (not possible since we need to check the condition)

5. **Conclusion:**
- The only bag that satisfies the condition \( B = 2W \) is Bag 4, which contains 6 balls.

### Final Answer:
The bag Ashutosh was talking about is **Bag 4**.