The mean temperature of Monday to Wednesday was `37^@C` and of Tuesday to Thursday was `34^@C` . If the temperature on Thursday was 4/5 that of Monday, the temperature of Thursday was

Options

A. `35.5^@C`
B. `34^@C`
C. `36.5^@C`
D. `36^@C`

Answer

To solve the problem step by step, we will use the information given about the average temperatures and the relationship between the temperatures on different days.

### Step-by-step Solution:

1. **Understanding the Averages**:
- The mean temperature from Monday to Wednesday is given as \(37^\circ C\).
- The mean temperature from Tuesday to Thursday is given as \(34^\circ C\).

2. **Calculating the Total Temperatures**:
- For Monday to Wednesday:
\[ \text{Mean} = \frac{\text{Sum of temperatures from Monday to Wednesday}}{3} = 37 \]
Therefore, the sum of temperatures from Monday to Wednesday is:
\[ \text{Sum} = 37 \times 3 = 111 \]
Let the temperatures be \(M\) (Monday), \(T\) (Tuesday), and \(W\) (Wednesday). Thus, we have:
\[ M + T + W = 111 \quad \text{(Equation 1)} \]

- For Tuesday to Thursday:
\[ \text{Mean} = \frac{\text{Sum of temperatures from Tuesday to Thursday}}{3} = 34 \]
Therefore, the sum of temperatures from Tuesday to Thursday is:
\[ \text{Sum} = 34 \times 3 = 102 \]
Let the temperatures be \(T\) (Tuesday), \(W\) (Wednesday), and \(H\) (Thursday). Thus, we have:
\[ T + W + H = 102 \quad \text{(Equation 2)} \]

3. **Setting Up the Equations**:
- We now have two equations:
- Equation 1: \(M + T + W = 111\)
- Equation 2: \(T + W + H = 102\)

4. **Subtracting the Equations**:
- To eliminate \(T\) and \(W\), we subtract Equation 2 from Equation 1:
\[ (M + T + W) - (T + W + H) = 111 - 102 \]
This simplifies to:
\[ M - H = 9 \quad \text{(Equation 3)} \]

5. **Using the Relationship Between Thursday and Monday**:
- We know that the temperature on Thursday \(H\) is \( \frac{4}{5} \) of Monday's temperature \(M\):
\[ H = \frac{4}{5}M \]

6. **Substituting into Equation 3**:
- Substitute \(H\) in Equation 3:
\[ M - \frac{4}{5}M = 9 \]
This simplifies to:
\[ \frac{1}{5}M = 9 \]
Therefore, multiplying both sides by 5 gives:
\[ M = 45 \]

7. **Finding Thursday's Temperature**:
- Now substitute \(M\) back into the equation for \(H\):
\[ H = \frac{4}{5}M = \frac{4}{5} \times 45 = 36 \]

### Final Answer:
The temperature on Thursday is \(36^\circ C\).

---