Follow the instructions below to answer the question.
Choose option a if the question can be answered by using data from Statement 1 alone
Choose option b if the question can be answered by using data from Statement 2 alone
Choose option c if the question can only be answered by using data from both 
Statements 
Choose option d if the question cannot be answered by using data from both Statements
Question – A sum of 77,000 was divided among Nimisha, Soumyadip, and Vaneet. 
Who received the least amount?
Statement 1 – Nimisha received 2/9 of what Soumyadip and Vaneet together received. 
Statement 2 – Soumyadip received 3/11 of what Nimisha and Vaneet together received. 

To determine who received the least amount, let's analyze the data provided in the statements step-by-step.

**Statement 1:** Nimisha received $ \frac{2}{9} $ of what Soumyadip and Vaneet together received.

Let:
- Nimisha's share be $ N $
- Soumyadip's share be $ S $
- Vaneet's share be $ V $

According to Statement 1:
\[ N = \frac{2}{9} (S + V) \]

**Statement 2:** Soumyadip received $ \frac{3}{11} $ of what Nimisha and Vaneet together received.

According to Statement 2:
\[ S = \frac{3}{11} (N + V) \]

Using the total amount distributed:
\[ N + S + V = 77000 \]

Let's substitute the expressions from the statements into this equation.

From Statement 1:
\[ N = \frac{2}{9} (S + V) \]

From Statement 2:
\[ S = \frac{3}{11} (N + V) \]

To solve for $ N $, $ S $, and $ V $:

1. From Statement 1: 
\[ N = \frac{2}{9} (S + V) \]
\[ 9N = 2(S + V) \]
\[ 9N = 2S + 2V \]

2. From Statement 2:
\[ S = \frac{3}{11} (N + V) \]
\[ 11S = 3(N + V) \]
\[ 11S = 3N + 3V \]

We now have three equations:
1. $ N + S + V = 77000 $
2. $ 9N = 2S + 2V $
3. $ 11S = 3N + 3V $

To find the shares:

1. Multiply the first equation by 9:
\[ 9N + 9S + 9V = 9 \times 77000 \]
\[ 9N + 9S + 9V = 693000 \]

2. We have $ 9N = 2S + 2V $:
\[ 2S + 2V = 9N \]

3. Rearrange the second equation to match the other variables:
\[ 9N + 9S + 9V = 693000 \]
\[ 11S = 3N + 3V \]

We can solve these simultaneous equations, but it's clear we need both equations to determine the specific values of $ N $, $ S $, and $ V $. 

Therefore, the answer to the question, "Who received the least amount?" can only be determined by using data from both statements. 

Hence, the correct answer is:

c. The question can only be answered by using data from both Statements

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. If Nimisha received $15,000, what did Soumyadip and Vaneet receive?
2. How would the total amount change if Vaneet's share was doubled?
3. What is the proportion of each person's share if the total amount was $100,000 instead of $77,000?
4. How does changing one share affect the overall distribution if the total amount remains constant?
5. What is the impact on Soumyadip's share if Nimisha's share is decreased by 10%?

**Tip:** When dealing with ratios and total sums, always set up equations based on given relationships and solve them step-by-step.

Learn how to solve a problem involving the division of a sum among three individuals. This problem requires understanding of algebraic concepts and ratios. Suitable for students in Grades 7-9.

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