The average weight A, B, C and D is 40 kg. A new person E is also included in the group, then the average weight of the group is increased by 1 kg. Again a new person F replaces A, then the new average of 5 persons becomes 42. Find the average weight of B, C, D, F.

Answer

To solve the problem step by step, let's break down the information given and find the required average weight of B, C, D, and F.

### Step 1: Calculate the total weight of A, B, C, and D
Given that the average weight of A, B, C, and D is 40 kg, we can calculate their total weight.

\[ \text{Average} = \frac{\text{Total Weight}}{\text{Number of Persons}} \]
\[ 40 = \frac{\text{Total Weight of A, B, C, D}}{4} \]

Multiplying both sides by 4:

\[ \text{Total Weight of A, B, C, D} = 40 \times 4 = 160 \text{ kg} \]

### Step 2: Include person E and calculate the new average
When person E is included, the average weight increases to 41 kg for 5 persons (A, B, C, D, and E).

\[ 41 = \frac{\text{Total Weight of A, B, C, D, E}}{5} \]

Multiplying both sides by 5:

\[ \text{Total Weight of A, B, C, D, E} = 41 \times 5 = 205 \text{ kg} \]

### Step 3: Calculate the weight of person E
Now, we can find the weight of person E by subtracting the total weight of A, B, C, and D from the total weight of A, B, C, D, and E.

\[ \text{Weight of E} = \text{Total Weight of A, B, C, D, E} - \text{Total Weight of A, B, C, D} \]
\[ \text{Weight of E} = 205 \text{ kg} - 160 \text{ kg} = 45 \text{ kg} \]

### Step 4: Replace A with F and calculate the new average
Now, person F replaces person A, and the new average weight of the 5 persons becomes 42 kg.

\[ 42 = \frac{\text{Total Weight of B, C, D, E, F}}{5} \]

Multiplying both sides by 5:

\[ \text{Total Weight of B, C, D, E, F} = 42 \times 5 = 210 \text{ kg} \]

### Step 5: Calculate the total weight of B, C, D, and F
We already know the total weight of A, B, C, and D is 160 kg. Since A is replaced by F, we can express the total weight of B, C, D, and F as:

\[ \text{Total Weight of B, C, D, F} = \text{Total Weight of A, B, C, D} - \text{Weight of A} + \text{Weight of F} \]

We can also express it as:

\[ \text{Total Weight of B, C, D, F} = \text{Total Weight of B, C, D, E, F} - \text{Weight of E} \]
\[ \text{Total Weight of B, C, D, F} = 210 \text{ kg} - 45 \text{ kg} = 165 \text{ kg} \]

### Step 6: Calculate the average weight of B, C, D, and F
Now, we can find the average weight of B, C, D, and F.

\[ \text{Average Weight of B, C, D, F} = \frac{\text{Total Weight of B, C, D, F}}{4} \]
\[ \text{Average Weight of B, C, D, F} = \frac{165 \text{ kg}}{4} = 41.25 \text{ kg} \]

### Final Answer
The average weight of B, C, D, and F is **41.25 kg**.