What was the total income of A in the year 2001?
(I) The total income of A in the year 1998. 1999, 2000 and 2001 was Rs 1 crore .
(II) Income of A is increased by 25% in successive year.

Options

A. If statement I alone is sufficient but statement Il alone is not sufficient.
B. If statement Il alone is sufficient but statement I alone is not sufficient.
C. If each statement alone (either I or II) is sufficient.
D. If both statement together are sufficient, but neither statement alone is sufficient.

Answer

To find the total income of A in the year 2001, we will analyze the information given in the two statements step by step.

### Step 1: Understand the Total Income Over the Years
We know from Statement (I) that the total income of A from the years 1998, 1999, 2000, and 2001 is Rs 1 crore (or Rs 1,00,00,000).

### Step 2: Define the Income for Each Year
Let’s denote the income for each year as follows:
- Income in 1998 = \( x \)
- Income in 1999 = \( x + 25\% \text{ of } x = x + 0.25x = 1.25x \)
- Income in 2000 = \( 1.25x + 25\% \text{ of } 1.25x = 1.25x + 0.25(1.25x) = 1.25x + 0.3125x = 1.5625x \)
- Income in 2001 = \( 1.5625x + 25\% \text{ of } 1.5625x = 1.5625x + 0.25(1.5625x) = 1.5625x + 0.390625x = 1.953125x \)

### Step 3: Set Up the Equation
Now, we can set up the equation based on the total income:
\[ x + 1.25x + 1.5625x + 1.953125x = 1,00,00,000 \]
Combining the terms:
\[ x(1 + 1.25 + 1.5625 + 1.953125) = 1,00,00,000 \]

### Step 4: Calculate the Coefficient
Calculating the sum of coefficients:
\[ 1 + 1.25 + 1.5625 + 1.953125 = 5.765625 \]
Thus, we have:
\[ 5.765625x = 1,00,00,000 \]

### Step 5: Solve for x
Now, we can solve for \( x \):
\[ x = \frac{1,00,00,000}{5.765625} \approx 17,371.42857 \]

### Step 6: Calculate Income for 2001
Now, we can find the income for the year 2001:
\[ \text{Income in 2001} = 1.953125x = 1.953125 \times 17,371.42857 \approx 33,333.33 \]

### Conclusion
Thus, the total income of A in the year 2001 is approximately Rs 33,333.33.

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