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 provided in the statements sufficient to answer the question. Read both the statements and give answer:
What is the cost price of the table?
I. The per cent profit earned when the table is sold for rs816 is three times the per cent profit earned when the table is sold for rs 672.
II. Had the cost price of the table been 20% less and had it been price sold for rs720, per cent profit earned would have been 50%.

Options

A. if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
B. if 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.
C. if the data in statement I alone or in statement II alone are sufficient to answer the question.
D. if the data in both the statementss I and II aree not sufficient to answer the question.

Answer

To solve the question regarding the cost price of the table, we will analyze the two statements provided and determine if either or both are sufficient to answer the question.

### Step-by-Step Solution:

1. **Understanding Statement I**:
- Statement I states that the percentage profit earned when the table is sold for Rs. 816 is three times the percentage profit earned when sold for Rs. 672.
- Let the cost price of the table be \( x \).
- The profit when sold for Rs. 816 can be expressed as:
\[ \text{Profit}_1 = 816 - x \]
The percentage profit when sold for Rs. 816 is:
\[ \text{Percentage Profit}_1 = \frac{(816 - x)}{x} \times 100 \]
- The profit when sold for Rs. 672 can be expressed as:
\[ \text{Profit}_2 = 672 - x \]
The percentage profit when sold for Rs. 672 is:
\[ \text{Percentage Profit}_2 = \frac{(672 - x)}{x} \times 100 \]
- According to Statement I:
\[ \frac{(816 - x)}{x} \times 100 = 3 \times \frac{(672 - x)}{x} \times 100 \]
- Simplifying this gives us:
\[ 816 - x = 3(672 - x) \]
\[ 816 - x = 2016 - 3x \]
\[ 2x = 1200 \implies x = 600 \]
- Thus, Statement I alone is sufficient to determine the cost price of the table.

2. **Understanding Statement II**:
- Statement II states that if the cost price of the table had been 20% less and sold for Rs. 720, the percentage profit would have been 50%.
- If the cost price is \( x \), then 20% less would be:
\[ \text{New Cost Price} = x - 0.2x = 0.8x \]
- The selling price is Rs. 720, and the profit is 50% of the new cost price:
\[ \text{Profit} = 0.5 \times (0.8x) = 0.4x \]
- The selling price can also be expressed as:
\[ \text{Selling Price} = \text{New Cost Price} + \text{Profit} \]
\[ 720 = 0.8x + 0.4x = 1.2x \]
- Solving for \( x \):
\[ x = \frac{720}{1.2} = 600 \]
- Thus, Statement II alone is also sufficient to determine the cost price of the table.

### Conclusion:
Both statements I and II are sufficient individually to determine the cost price of the table. Therefore, the answer is:

**Option 3: Each statement alone is sufficient.**

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