Each question consists of a question and two statements I and II given below it You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and choose the appropriate option.
Whatis the cost price of the table which is marked at ₹x?
I. On giving a discount of ₹1200, a profit of `20%` is earned.
II. Had there been no discount on the table, a profit of ₹1500 would have been earned.

Options

A. The data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question.
B. The data either in statement I alone or in statement II alone are sufficient to answer the question.
C. The data in both the statements I and II together are not sufficient to answer the question.
D. The data in both the statements I and II together are necessary to answer the question.

Answer

To solve the problem, we need to analyze the information given in both statements and see if they provide enough data to determine the cost price of the table marked at ₹x.

### Step-by-Step Solution:

1. **Understanding the Question**:
We need to find the cost price (CP) of a table that is marked at ₹x.

2. **Analyzing Statement I**:
- Statement I states that on giving a discount of ₹1200, a profit of 20% is earned.
- Let the cost price be CP.
- The selling price (SP) after the discount would be:
\[ SP = x - 1200 \]
- Since there is a profit of 20%, we can express this as:
\[ SP = CP + 0.2 \times CP = 1.2 \times CP \]
- Therefore, we have:
\[ x - 1200 = 1.2 \times CP \quad \text{(Equation 1)} \]

3. **Analyzing Statement II**:
- Statement II states that had there been no discount on the table, a profit of ₹1500 would have been earned.
- In this case, the selling price would simply be the marked price:
\[ SP = x \]
- The profit of ₹1500 means:
\[ SP = CP + 1500 \]
- Therefore, we have:
\[ x = CP + 1500 \quad \text{(Equation 2)} \]

4. **Combining the Information**:
- We now have two equations:
- From Statement I: \( x - 1200 = 1.2 \times CP \)
- From Statement II: \( x = CP + 1500 \)
- We can substitute Equation 2 into Equation 1:
\[ (CP + 1500) - 1200 = 1.2 \times CP \]
- Simplifying this gives:
\[ CP + 300 = 1.2 \times CP \]
- Rearranging gives:
\[ 300 = 1.2 \times CP - CP \]
\[ 300 = 0.2 \times CP \]
- Thus, we find:
\[ CP = \frac{300}{0.2} = 1500 \]

5. **Conclusion**:
- We have successfully determined the cost price of the table, which is ₹1500.
- Therefore, both statements together are necessary to answer the question.

### Final Answer:
The data in both statements (I and II) together are necessary to answer the question.