Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer.
Find the cost price of the article.
Statement I: The article is marked up by T% and it is sold at discount of 20%. The profit earned on selling the article is 44%.
Statement II: If shopkeeper offers a discount of 40% on marked price, then he earns the profit of Rs. 16
Statement III: If shopkeeper doesn't offer any discount on marked price, then the selling price will be Rs. 160 more than the cost price of the article.

Options

A. Only the data given in statements I and II together is sufficient to answer the question.
B. Only the data given in statements I and III together is sufficient to answer the question.
C. The data given in any two statements together is sufficient to answer the question
D. The data given in all three statements I, II and III together is sufficient to answer the question.

Explanation

To find the cost price of the article using the provided statements, we can analyze each statement step by step.

### Step 1: Analyze Statement I
Statement I states that the article is marked up by T% and sold at a discount of 20%. The profit earned on selling the article is 44%.

Let:
- Cost Price (C) = C
- Marked Price (M) = C * (1 + T/100)
- Selling Price (S) = M * (1 - 20/100) = M * 0.8

From the profit information:
Profit = Selling Price - Cost Price = 44% of Cost Price
So, we can write:
\[ S = C + 0.44C = 1.44C \]

Equating the two expressions for Selling Price:
\[ M * 0.8 = 1.44C \]
Substituting M:
\[ (C * (1 + T/100)) * 0.8 = 1.44C \]
Dividing both sides by C (assuming C ≠ 0):
\[ (1 + T/100) * 0.8 = 1.44 \]
From this, we can solve for T:
\[ 1 + T/100 = \frac{1.44}{0.8} = 1.8 \]
\[ T/100 = 1.8 - 1 = 0.8 \]
\[ T = 80\% \]

### Step 2: Analyze Statement II
Statement II states that if the shopkeeper offers a discount of 40% on the marked price, then he earns a profit of Rs. 16.

Using the same definitions:
- Selling Price with 40% discount = M * (1 - 40/100) = M * 0.6

From the profit information:
Profit = Selling Price - Cost Price = Rs. 16
So, we can write:
\[ S = C + 16 \]

Equating the two expressions for Selling Price:
\[ M * 0.6 = C + 16 \]
Substituting M from Step 1:
\[ (C * (1 + 80/100)) * 0.6 = C + 16 \]
\[ (C * 1.8) * 0.6 = C + 16 \]
\[ 1.08C = C + 16 \]
\[ 1.08C - C = 16 \]
\[ 0.08C = 16 \]
\[ C = \frac{16}{0.08} = 200 \]

### Step 3: Analyze Statement III
Statement III states that if the shopkeeper doesn't offer any discount on the marked price, then the selling price will be Rs. 160 more than the cost price of the article.

Using the definitions:
- Selling Price without discount = M

From the profit information:
Profit = Selling Price - Cost Price = Rs. 160
So, we can write:
\[ M = C + 160 \]

Substituting M from Step 1:
\[ C * (1 + 80/100) = C + 160 \]
\[ 1.8C = C + 160 \]
\[ 1.8C - C = 160 \]
\[ 0.8C = 160 \]
\[ C = \frac{160}{0.8} = 200 \]

### Conclusion
From the analysis of all three statements, we can conclude that:
- The cost price of the article is Rs. 200.