Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provident in the statements is sufficient to answer the question. Read both statements and-
How many marks did Neha get in History ?
I. Average marks obtained by Neha in History. Maths and English is equal to the average marks in Maths and English
II. Neha got a total of 120 marks in Maths and ENglish together ?

Options

A. If the data in statement I along is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
C. If the data in statement I alone or statement II alone is sufficient to answer the question.
D. If the data in both the statements I and II together is necessary to answer the question.

Answer

To determine how many marks Neha got in History, we will analyze the two statements provided.

**Step 1: Analyze Statement I**
- Statement I says: "The average marks obtained by Neha in History, Maths, and English is equal to the average marks in Maths and English."
- Let’s denote:
- Marks in History = h
- Marks in Maths = m
- Marks in English = e
- The average of History, Maths, and English can be expressed as:
\[ \text{Average of (h, m, e)} = \frac{h + m + e}{3} \]
- The average of Maths and English can be expressed as:
\[ \text{Average of (m, e)} = \frac{m + e}{2} \]
- According to Statement I, these two averages are equal:
\[ \frac{h + m + e}{3} = \frac{m + e}{2} \]
- Cross-multiplying gives:
\[ 2(h + m + e) = 3(m + e) \]
- Expanding both sides:
\[ 2h + 2m + 2e = 3m + 3e \]
- Rearranging gives:
\[ 2h = 3m + 3e - 2m - 2e \implies 2h = m + e \]
- From this, we can express h in terms of m and e:
\[ h = \frac{m + e}{2} \]
- However, we do not have specific values for m and e, so we cannot determine the exact value of h. Therefore, Statement I alone is insufficient.

**Step 2: Analyze Statement II**
- Statement II states: "Neha got a total of 120 marks in Maths and English together."
- This can be expressed as:
\[ m + e = 120 \]
- While this gives us the total marks in Maths and English, it does not provide any information about the marks in History (h). Therefore, Statement II alone is also insufficient.

**Step 3: Analyze Both Statements Together**
- Now, if we combine both statements, we have:
- From Statement I: \( h = \frac{m + e}{2} \)
- From Statement II: \( m + e = 120 \)
- Substituting the value of \( m + e \) from Statement II into the equation from Statement I:
\[ h = \frac{120}{2} = 60 \]
- Thus, when we use both statements together, we can determine that Neha got 60 marks in History.

**Conclusion:**
The answer to the question "How many marks did Neha get in History?" is 60 marks.