The following questions are accopanied by three statements (A) or (I), (B) or (II), and (C) or (III). You have to determine which statement(s) is/are sufficient/necessary to answer the questions.
To find the temperature on Monday which of the following information is sufficient?
A. The average temperature for Monday, Tuesday and Wednesday was `38^(@)C. `
B. The average temperature for Tuesday, Wednesday i and Thursday was `43^(@)`
C. The temperature on Tuesday and Thursday was ` 45^(@) C `each.

Options

A. Only A and B are sufficient
B. Only B and Care sufficient
C. A and either B or Care sufficient
D. All the three together are sufficient

Answer

To determine the temperature on Monday, we need to analyze the information provided in the three statements (A, B, and C) and see if they are sufficient to find the temperature.

### Step-by-Step Solution:

1. **Analyze Statement A:**
- Statement A states that the average temperature for Monday, Tuesday, and Wednesday was \(38^\circ C\).
- To find the total temperature for these three days, we can use the formula for average:
\[ \text{Average} = \frac{\text{Sum of temperatures}}{\text{Number of days}} \]
- Thus, we have:
\[ 38 = \frac{M + T + W}{3} \]
- Where \(M\) is the temperature on Monday, \(T\) is the temperature on Tuesday, and \(W\) is the temperature on Wednesday.
- Rearranging gives:
\[ M + T + W = 38 \times 3 = 114 \]
- So, \(M + T + W = 114\). This alone does not provide enough information to find \(M\) since we have two unknowns (\(T\) and \(W\)).

**Hint for Step 1:** Check if the average gives you a total sum and if you can isolate the variable you need.

2. **Analyze Statement B:**
- Statement B states that the average temperature for Tuesday, Wednesday, and Thursday was \(43^\circ C\).
- Using the same average formula:
\[ 43 = \frac{T + W + Th}{3} \]
- Thus, we have:
\[ T + W + Th = 43 \times 3 = 129 \]
- So, \(T + W + Th = 129\). Again, we cannot isolate \(M\) with this information alone since we have three unknowns.

**Hint for Step 2:** Consider how the second statement relates to the first and if it helps in finding the unknown.

3. **Analyze Statement C:**
- Statement C states that the temperature on Tuesday and Thursday was \(45^\circ C\) each.
- Therefore, we have:
\[ T = 45 \quad \text{and} \quad Th = 45 \]
- Now we can substitute \(T\) into the equation from Statement A:
\[ M + 45 + W = 114 \]
- Rearranging gives:
\[ M + W = 114 - 45 = 69 \quad \text{(Equation 1)} \]
- We can also substitute \(T\) into the equation from Statement B:
\[ 45 + W + 45 = 129 \]
- Simplifying gives:
\[ W + 90 = 129 \implies W = 129 - 90 = 39 \quad \text{(Equation 2)} \]

4. **Finding \(M\):**
- Now we can use Equation 1 and substitute \(W\):
\[ M + 39 = 69 \]
- Rearranging gives:
\[ M = 69 - 39 = 30 \]

Thus, the temperature on Monday is \(30^\circ C\).

### Conclusion:
To find the temperature on Monday, we needed all three statements (A, B, and C) together. Therefore, the answer is that all three statements combined are sufficient to determine the temperature on Monday.