In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.
What is the number of students who are good in either Hindi or Mathematics but not in English?

Options

A. 99
B. 107
C. 125
D. 130

Answer

To solve the problem step by step, we need to analyze the information given about the students in different subjects and apply the principle of inclusion-exclusion.

### Step 1: Identify the numbers given in the problem
- Students good in Hindi only (H) = 54
- Students good in Mathematics only (M) = 63
- Students good in English only (E) = 41
- Students good in both Hindi and Mathematics (H ∩ M) = 18
- Students good in all three subjects (H ∩ M ∩ E) = 10

### Step 2: Calculate the number of students good in Hindi or Mathematics
We want to find the number of students who are good in either Hindi or Mathematics, but not in English.

To do this, we first need to find the total number of students who are good in Hindi or Mathematics. This can be represented as:
\[ \text{Total (H ∪ M)} = \text{Students good in Hindi only} + \text{Students good in Mathematics only} + \text{Students good in both Hindi and Mathematics} \]
So,
\[ \text{Total (H ∪ M)} = H + M + (H ∩ M) \]
Substituting the values:
\[ \text{Total (H ∪ M)} = 54 + 63 + 18 \]
Calculating this gives:
\[ \text{Total (H ∪ M)} = 135 \]

### Step 3: Subtract the students who are good in all three subjects
Now, we need to exclude the students who are good in English as well. The number of students who are good in all three subjects is given as 10. Therefore, we subtract these students from our total:
\[ \text{Students good in either Hindi or Mathematics but not in English} = \text{Total (H ∪ M)} - \text{Students good in all three subjects} \]
So,
\[ \text{Students good in either Hindi or Mathematics but not in English} = 135 - 10 \]
Calculating this gives:
\[ \text{Students good in either Hindi or Mathematics but not in English} = 125 \]

### Final Answer
Thus, the number of students who are good in either Hindi or Mathematics but not in English is **125**.