The marks of 3 students A, B and C are in the ratio 10:12:15. If the maximum marks of the paper are 100, then the marks o fB cannot be in the range of

Options

A. 20-30
B. 40-50
C. 70-80
D. 80-90

Answer

To solve the problem, we need to determine the range of marks that student B can achieve based on the given ratio of marks for students A, B, and C. The marks are in the ratio of 10:12:15, and the maximum marks for the paper are 100.

### Step-by-Step Solution:

1. **Understanding the Ratio**:
The marks of students A, B, and C are given in the ratio 10:12:15. This means:
- Marks of A = 10x
- Marks of B = 12x
- Marks of C = 15x
where x is a common multiplier.

2. **Finding the Maximum Marks**:
Since the maximum marks for the paper are 100, we need to ensure that the marks for each student do not exceed this limit.

3. **Calculating Maximum Value of x**:
To find the maximum value of x, we can set the maximum marks for C (the highest ratio) to 100:
\[ 15x \leq 100 \]
Solving for x:
\[ x \leq \frac{100}{15} \approx 6.67 \]

4. **Determining Maximum Marks for B**:
Now, we will calculate the maximum marks for B using the maximum value of x:
\[ \text{Maximum marks for B} = 12x \]
Substituting the maximum value of x:
\[ \text{Maximum marks for B} = 12 \times 6.67 \approx 80 \]

5. **Finding the Range of Marks for B**:
Since x can take values from 0 to approximately 6.67, we can find the minimum and maximum marks for B:
- Minimum marks for B (when x=0) = 0
- Maximum marks for B (when x=6.67) = 80

Therefore, the possible range of marks for B is from 0 to 80.

6. **Identifying the Range B Cannot Be In**:
Since the maximum marks for B can be at most 80, B cannot have marks in the range above 80. Therefore, any range that includes values greater than 80 is not possible for B.

### Conclusion:
The marks of B cannot be in the range of 80 to 90.