Each question below is followed by two Statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer
What is Nikita's share in the profit of Rs. 50000 earned in the business run by her in partnership with Sharmila?
I Nikita invested an amount 150% of the amount invested by Sharmila.
​II. The amount invested by Sharmila is two-third of the amount invested by Nikita.

Options

A. if the Statement I alone is sufficient to answer the question but the Statement II alone is not sufficient
B. if the Statement II alone is sufficient to answer the question but the Statement I alone is not sufficient
C. if both Statement I and II together are needed to answer the question
D. if either the Statement I alone or Statement II alone is to sufficient to answer the question

Answer

To determine Nikita's share in the profit of Rs. 50,000 earned in the business run in partnership with Sharmila, we need to analyze the information provided in Statements I and II.

### Step 1: Analyze Statement I
Statement I states that "Nikita invested an amount 150% of the amount invested by Sharmila."

Let the amount invested by Sharmila be denoted as \( S \).
Then, according to Statement I, the amount invested by Nikita \( N \) can be expressed as:
\[ N = 1.5S \]

### Step 2: Analyze Statement II
Statement II states that "The amount invested by Sharmila is two-thirds of the amount invested by Nikita."

This can be expressed mathematically as:
\[ S = \frac{2}{3}N \]

### Step 3: Relate the Two Statements
Now we have two equations from the statements:
1. From Statement I: \( N = 1.5S \)
2. From Statement II: \( S = \frac{2}{3}N \)

We can substitute \( N \) from the first equation into the second equation:
\[ S = \frac{2}{3}(1.5S) \]
\[ S = \frac{2 \times 1.5}{3}S \]
\[ S = \frac{3}{3}S \]
This simplifies to \( S = S \), which is always true, indicating that both statements are consistent with each other.

### Step 4: Calculate the Profit Share
To find Nikita's share in the profit, we need to determine the ratio of their investments:
From Statement I, we have:
\[ N = 1.5S \]

The total investment \( T \) is:
\[ T = N + S = 1.5S + S = 2.5S \]

Now, the share of profit is distributed in the ratio of their investments:
- Nikita's share = \( \frac{N}{T} \times \text{Total Profit} \)
- Sharmila's share = \( \frac{S}{T} \times \text{Total Profit} \)

Calculating Nikita's share:
\[ \text{Nikita's share} = \frac{1.5S}{2.5S} \times 50000 \]
\[ = \frac{1.5}{2.5} \times 50000 \]
\[ = \frac{3}{5} \times 50000 \]
\[ = 30000 \]

### Conclusion
Nikita's share in the profit of Rs. 50,000 is Rs. 30,000.