In each of the following questions, a is followed by information given in three statements. You have to decide the information given in which of the statements is necessary and sufficient to answer the question.
The company earned how much profit in the year 2002 ?
(1) In 2001 the company earned `40%` more profit which earned in the year 2003
(2) The company earned the profit of 20 crores together in the year 2001 and 2002
(3) The company earned in 2003, `80%` profit which was earned in the year 2002 .

Options

A. Any two of (1), (2) and (3) are sufficient
B. Either (1) and (2) or (2) and (3) are sufficient
C. (1) and (2) or (3) are sufficient
D. (1), (2) and (3) all the three are necessary to answer

Answer

To determine the profit earned by the company in the year 2002, we will analyze the information given in the three statements step by step.

### Step 1: Define Variables
Let:
- Profit in 2001 = \( x \)
- Profit in 2002 = \( y \)
- Profit in 2003 = \( z \)

### Step 2: Analyze Statement 1
From statement (1), we know:
- In 2001, the company earned 40% more profit than in 2003.
- This can be expressed as:
\[ x = 1.4z \]

### Step 3: Analyze Statement 2
From statement (2), we have:
- The company earned a total profit of 20 crores in 2001 and 2002 combined.
- This can be expressed as:
\[ x + y = 20 \text{ crores} \]

### Step 4: Analyze Statement 3
From statement (3), we know:
- The company earned 80% of the profit in 2002 in the year 2003.
- This can be expressed as:
\[ z = 0.8y \]

### Step 5: Substitute and Solve
Now we will substitute the expressions from statements (1) and (3) into statement (2).

1. From statement (3), substitute \( z \) in statement (1):
\[ x = 1.4(0.8y) = 1.12y \]

2. Substitute \( x \) into statement (2):
\[ 1.12y + y = 20 \]
\[ 2.12y = 20 \]
\[ y = \frac{20}{2.12} = \frac{2000}{212} \approx 9.43 \text{ crores} \]

### Step 6: Conclusion
Thus, the profit earned by the company in the year 2002 is approximately \( 9.43 \) crores.

### Summary of Necessary Statements
To find the profit in 2002, we needed all three statements:
1. Statement (1) provided the relationship between profits in 2001 and 2003.
2. Statement (2) gave the total profit for 2001 and 2002.
3. Statement (3) connected the profits of 2002 and 2003.