Among four bags, average weight of last three bags Is 18 kg and the average weight of first three bags is 19 kg. If the weight of last bag is 22 kg, then what is the weight (in kg) of first bag?

Options

A. 32
B. 24
C. 33
D. 25

Answer

To solve the problem step by step, we will use the information provided about the average weights of the bags.

### Step 1: Calculate the total weight of the last three bags (B, C, D)
The average weight of the last three bags (B, C, D) is given as 18 kg.

Using the formula for average:
\[ \text{Average} = \frac{\text{Total Weight}}{\text{Number of Items}} \]
we can rearrange it to find the total weight:
\[ \text{Total Weight} = \text{Average} \times \text{Number of Items} \]
Substituting the values:
\[ B + C + D = 18 \times 3 = 54 \text{ kg} \]

### Step 2: Calculate the total weight of the first three bags (A, B, C)
The average weight of the first three bags (A, B, C) is given as 19 kg.

Using the same formula:
\[ A + B + C = 19 \times 3 = 57 \text{ kg} \]

### Step 3: Substitute the weight of the last bag (D)
We know that the weight of the last bag (D) is 22 kg.

Now we can substitute D into the equation from Step 1:
\[ B + C + 22 = 54 \]
From this, we can find \(B + C\):
\[ B + C = 54 - 22 = 32 \text{ kg} \]

### Step 4: Substitute \(B + C\) into the equation from Step 2
Now we will substitute \(B + C\) into the equation from Step 2:
\[ A + (B + C) = 57 \]
Substituting \(B + C = 32\):
\[ A + 32 = 57 \]

### Step 5: Solve for A
Now, we can solve for A:
\[ A = 57 - 32 = 25 \text{ kg} \]

### Final Answer
The weight of the first bag (A) is **25 kg**.

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