Each of the following question is followed by two statements I , and II. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
In how much time can Deepika do the work alone?
I. Kareena & Deepika can complete a piece of work in 10 days working together.
II. Madhuri and Kareena can complete the work in 6 days working together.

Options

A. A)Only Statement I alone.
B. B)Only Statement II alone.
C. C) Both Statements I and II together.
D. D)Neither Statement I nor II is sufficient.

Answer

To solve the question, we need to determine how much time Deepika can complete the work alone based on the provided statements.

### Step-by-Step Solution:

1. **Understanding the Question**:
We need to find out how long Deepika takes to complete the work alone.

2. **Analyzing Statement I**:
- Statement I states that Kareena and Deepika can complete the work together in 10 days.
- This means their combined work rate is \( \frac{1}{10} \) of the work per day.
- However, we do not have any information about how long Kareena can complete the work alone. Therefore, this statement alone is not sufficient to determine how long Deepika can complete the work alone.

**Hint**: Consider the combined work rate and the need for individual work rates to find the answer.

3. **Analyzing Statement II**:
- Statement II states that Madhuri and Kareena can complete the work together in 6 days.
- This means their combined work rate is \( \frac{1}{6} \) of the work per day.
- Similar to Statement I, we do not have information about how long Madhuri or Kareena can complete the work alone. Therefore, this statement alone is also not sufficient to determine how long Deepika can complete the work alone.

**Hint**: Think about how knowing the combined work rate of different pairs helps in finding individual work rates.

4. **Combining Both Statements**:
- From Statement I, we know Kareena and Deepika's combined efficiency is \( \frac{1}{10} \) of the work per day.
- From Statement II, we know Madhuri and Kareena's combined efficiency is \( \frac{1}{6} \) of the work per day.
- To find individual efficiencies, we would need more information about the individual work rates of either Kareena or Madhuri, which we do not have.

**Hint**: Combining statements can sometimes yield more information, but here we still lack individual efficiencies.

5. **Conclusion**:
- Since neither statement provides sufficient information on their own or when combined to determine how long Deepika can complete the work alone, we conclude that neither statement is sufficient.

### Final Answer:
The answer is **Option D**: Neither statement I nor II is sufficient to answer the question.