The average temperature of Monday Tuesday Wednesday and Thursday was `38^@`and that of Tuesday Wednesday Thursday and Friday was `40^@` if the temperature on Monday was `30^@` the temperature of Friday was

Options

A. `40^@`
B. `39^@`
C. `38^@`
D. `30^@`

Answer

To find the temperature on Friday based on the given information, we can follow these steps:

### Step 1: Calculate the total temperature for Monday, Tuesday, Wednesday, and Thursday

The average temperature for Monday, Tuesday, Wednesday, and Thursday is given as \(38^\circ\). Since there are four days, we can calculate the total temperature for these four days.

\[ \text{Total temperature (Monday + Tuesday + Wednesday + Thursday)} = \text{Average} \times \text{Number of days} = 38 \times 4 = 152 \]

### Step 2: Set up the equation for the total temperature

Let the temperatures of Tuesday, Wednesday, and Thursday be \(T_2\), \(T_3\), and \(T_4\) respectively. We can express the total temperature as:

\[ 30 + T_2 + T_3 + T_4 = 152 \]

### Step 3: Simplify the equation

From the equation above, we can isolate the sum of the temperatures for Tuesday, Wednesday, and Thursday:

\[ T_2 + T_3 + T_4 = 152 - 30 = 122 \]

### Step 4: Calculate the total temperature for Tuesday, Wednesday, Thursday, and Friday

The average temperature for Tuesday, Wednesday, Thursday, and Friday is given as \(40^\circ\). Therefore, we can calculate the total temperature for these four days:

\[ \text{Total temperature (Tuesday + Wednesday + Thursday + Friday)} = 40 \times 4 = 160 \]

### Step 5: Set up the equation for the total temperature including Friday

Using the same variables, we can express the total temperature including Friday:

\[ T_2 + T_3 + T_4 + T_5 = 160 \]

Where \(T_5\) is the temperature on Friday.

### Step 6: Substitute the known value of \(T_2 + T_3 + T_4\)

Now we can substitute the value we found for \(T_2 + T_3 + T_4\) into this equation:

\[ 122 + T_5 = 160 \]

### Step 7: Solve for \(T_5\)

Now, we can isolate \(T_5\) to find the temperature on Friday:

\[ T_5 = 160 - 122 = 38 \]

### Conclusion

The temperature on Friday is \(38^\circ\).