In ABC corporation there are some management trainees. These trainess, are divided into 3 groups A, B and C for 3 different projects in the ratio of 3 : 4 : 5 respectively, where P, Q, R are the projects-in-charge of A, B, C respectively. The difference between the no. of trainees in A and C is not greater than 3. Also P, Q, R belongs to the group of trainess. The no. of assistant of Q is less than the no. of assistance of R by :

Options

A. `33.33%`
B. `20%`
C. `25%`
D. `16.66%`

Answer

To solve the problem, we need to break down the information given and find the number of trainees in each group A, B, and C, and then determine the number of assistants for Q and R.

### Step-by-Step Solution:

1. **Understanding the Ratio:**
The trainees are divided into three groups A, B, and C in the ratio of 3:4:5.
Let's denote the number of trainees in group A as \(3x\), in group B as \(4x\), and in group C as \(5x\), where \(x\) is a common multiplier.

2. **Setting Up the Equation:**
According to the problem, the difference between the number of trainees in A and C should not be greater than 3. Therefore, we can write:
\[ |3x - 5x| \leq 3 \]
This simplifies to:
\[ | -2x | \leq 3 \quad \Rightarrow \quad 2x \leq 3 \]

3. **Solving for x:**
Dividing both sides by 2 gives:
\[ x \leq \frac{3}{2} = 1.5 \]
Since \(x\) must be a whole number (as we can't have a fraction of a trainee), the possible values for \(x\) are 1.

4. **Calculating the Number of Trainees:**
If \(x = 1\):
- Number of trainees in A = \(3x = 3 \times 1 = 3\)
- Number of trainees in B = \(4x = 4 \times 1 = 4\)
- Number of trainees in C = \(5x = 5 \times 1 = 5\)

5. **Verifying the Difference:**
Now, we check the difference between A and C:
\[ |3 - 5| = 2 \]
This satisfies the condition that the difference is not greater than 3.

6. **Finding the Number of Assistants:**
The problem states that P, Q, and R are part of the trainees.
- Let’s assume Q has 3 assistants (since Q is alone, we can assume he has 3 assistants).
- R has 4 assistants (since R is one of the trainees).

7. **Calculating the Difference in Assistants:**
The difference between the number of assistants of Q and R is:
\[ 4 - 3 = 1 \]

8. **Finding the Percentage Difference:**
To find the percentage difference between the assistants of Q and R:
\[ \text{Percentage Difference} = \left(\frac{4 - 3}{4}\right) \times 100 = \left(\frac{1}{4}\right) \times 100 = 25\% \]

### Final Answer:
The number of assistants of Q is less than the number of assistants of R by 1, which is 25%.