Following are the questions based on two statements and answer the following based on the given statements.
What will be cost price of article, which marked 40% above.
Statement I. If article sold 25% discount profit will be Rs. 50.
Statement II. If article sold two successive discounts of `14(2)/(7)%` and 10% profit will be Rs. 80.

Options

A. A)Only statement I is sufficient
B. B)Either statement I
or Statement II alone
is sufficient
C. C)Statement I and II
both together is sufficient
D. D)Only statement II is sufficient

Answer

To solve the problem, we need to determine the cost price of an article that is marked 40% above its cost price. We will analyze the two statements provided to see if either one alone, or both together, can give us the answer.

### Step 1: Understand the Marked Price (MP) and Cost Price (CP)
Let the cost price (CP) of the article be \( x \).
Since the article is marked 40% above the cost price, the marked price (MP) will be:
\[ MP = CP + 40\% \text{ of } CP = x + 0.4x = 1.4x \]

### Step 2: Analyze Statement I
**Statement I:** If the article is sold at a 25% discount, the profit will be Rs. 50.

1. Calculate the selling price (SP) after a 25% discount on the marked price:
\[ SP = MP - 25\% \text{ of } MP = MP - 0.25 \times MP = 0.75 \times MP = 0.75 \times 1.4x = 1.05x \]

2. Profit is given as Rs. 50, which can be expressed as:
\[ SP - CP = 50 \implies 1.05x - x = 50 \implies 0.05x = 50 \]

3. Solve for \( x \):
\[ x = \frac{50}{0.05} = 1000 \]

### Conclusion from Statement I
From Statement I, we find that the cost price (CP) is Rs. 1000.

### Step 3: Analyze Statement II
**Statement II:** If the article is sold with two successive discounts of \( 14\frac{2}{7}\% \) and 10%, the profit will be Rs. 80.

1. Convert \( 14\frac{2}{7}\% \) to a fraction:
\[ 14\frac{2}{7}\% = \frac{100}{7}\% = \frac{100}{700} = \frac{1}{7} \]

2. Calculate the selling price (SP) after applying the two discounts:
- First discount of \( \frac{1}{7} \):
\[ SP_1 = MP \times \left(1 - \frac{1}{7}\right) = MP \times \frac{6}{7} = 1.4x \times \frac{6}{7} = \frac{8.4x}{7} \]

- Second discount of 10%:
\[ SP_2 = SP_1 \times \left(1 - 0.1\right) = SP_1 \times 0.9 = \frac{8.4x}{7} \times 0.9 = \frac{8.4 \times 0.9x}{7} = \frac{7.56x}{7} = 1.08x \]

3. Profit is given as Rs. 80:
\[ SP - CP = 80 \implies 1.08x - x = 80 \implies 0.08x = 80 \]

4. Solve for \( x \):
\[ x = \frac{80}{0.08} = 1000 \]

### Conclusion from Statement II
From Statement II, we also find that the cost price (CP) is Rs. 1000.

### Final Conclusion
Both statements independently lead to the same conclusion regarding the cost price of the article.

### Answer
The cost price of the article is Rs. 1000.