Which of the following statements is correct?
tatement-1 : Mrs Soni bought `7 1/2` litres of milk. Out of this, `5 3/4` litres was consumed. `1 1/3` litres of milk is left with her.
Statement-2 : Amit reads `(3)/(5)` of a book. He finds that there are still 80 pages left to be read. Total number of pages in the book is 200.

Options

A. Only Statement-1
B. Only Statement-2
C. Both Statement-1 and Statement-2
D. Neither Statement-1 and nor Statement-2

Explanation

To determine which of the statements is correct, we will analyze both statements step by step.

### Statement 1:
Mrs. Soni bought `7 1/2` litres of milk. Out of this, `5 3/4` litres was consumed. We need to check if `1 1/3` litres of milk is left with her.

**Step 1: Convert mixed numbers to improper fractions.**
- `7 1/2` litres can be converted:
\[ 7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2} \text{ litres} \]
- `5 3/4` litres can be converted:
\[ 5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4} \text{ litres} \]
- `1 1/3` litres can be converted:
\[ 1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3} \text{ litres} \]

**Step 2: Calculate the remaining milk after consumption.**
- Remaining milk = Total milk - Consumed milk
\[ \text{Remaining milk} = \frac{15}{2} - \frac{23}{4} \]
- To subtract these fractions, we need a common denominator. The least common multiple of 2 and 4 is 4.
- Convert `15/2` to have a denominator of 4:
\[ \frac{15}{2} = \frac{15 \times 2}{2 \times 2} = \frac{30}{4} \]
- Now subtract:
\[ \frac{30}{4} - \frac{23}{4} = \frac{30 - 23}{4} = \frac{7}{4} \text{ litres} \]

**Step 3: Compare the calculated remaining milk with the given remaining milk.**
- We found that the remaining milk is `7/4` litres.
- Convert `7/4` to a mixed number:
\[ \frac{7}{4} = 1 \frac{3}{4} \]
- The statement claims that `1 1/3` litres is left, which is not equal to `1 3/4`. Therefore, Statement 1 is incorrect.

### Statement 2:
Amit reads `(3/5)` of a book and finds that there are still 80 pages left to be read. We need to verify if the total number of pages in the book is 200.

**Step 1: Let the total number of pages be \( P \).**
- According to the problem, if Amit reads `(3/5)` of the book, then the pages he has read can be expressed as:
\[ \text{Pages read} = \frac{3}{5}P \]
- The remaining pages are:
\[ \text{Remaining pages} = P - \frac{3}{5}P = \frac{2}{5}P \]
- We know from the problem that the remaining pages equal 80:
\[ \frac{2}{5}P = 80 \]

**Step 2: Solve for \( P \).**
- Multiply both sides by 5 to eliminate the fraction:
\[ 2P = 80 \times 5 \]
\[ 2P = 400 \]
- Now divide by 2:
\[ P = \frac{400}{2} = 200 \]

**Step 3: Check the calculation.**
- If the total number of pages is 200, then the pages read would be:
\[ \frac{3}{5} \times 200 = 120 \text{ pages} \]
- The remaining pages would be:
\[ 200 - 120 = 80 \text{ pages} \]
- This matches the information given in the statement.

### Conclusion:
- Statement 1 is incorrect.
- Statement 2 is correct.

Thus, the correct answer is that **only Statement 2 is correct**.