The average temperature for Monday ,Wednesday and Frinday was `41^(@)C` .The average for Wednesday ,Frinday and Thursday was `42^(@)C` .If the temperature on Thursday was `43^(@)C` , then the temperature on Monday was :

Options

A. `41^(@)C`
B. `42^(@)C`
C. `46^(@)C`
D. `40^(@)C`

Answer

To solve the problem step by step, we will denote the temperatures as follows:

- Let \( M \) be the temperature on Monday.
- Let \( W \) be the temperature on Wednesday.
- Let \( F \) be the temperature on Friday.
- Let \( T \) be the temperature on Thursday.

### Step 1: Set up the equations based on the averages given.

1. The average temperature for Monday, Wednesday, and Friday is \( 41^\circ C \):
\[ \frac{M + W + F}{3} = 41 \]
Multiplying both sides by 3:
\[ M + W + F = 123 \quad \text{(Equation 1)} \]

2. The average temperature for Wednesday, Friday, and Thursday is \( 42^\circ C \):
\[ \frac{W + F + T}{3} = 42 \]
Multiplying both sides by 3:
\[ W + F + T = 126 \quad \text{(Equation 2)} \]

### Step 2: Substitute the known value for Thursday's temperature.

We know that the temperature on Thursday \( T = 43^\circ C \). Substituting this value into Equation 2:
\[ W + F + 43 = 126 \]
Subtracting 43 from both sides:
\[ W + F = 83 \quad \text{(Equation 3)} \]

### Step 3: Substitute Equation 3 into Equation 1.

Now we will substitute Equation 3 into Equation 1:
\[ M + (W + F) = 123 \]
Substituting \( W + F = 83 \):
\[ M + 83 = 123 \]
Subtracting 83 from both sides:
\[ M = 123 - 83 \]
Calculating the right side:
\[ M = 40 \]

### Conclusion

The temperature on Monday is \( 40^\circ C \).