There are three sections A, B and C in class X of a school. The average weight of all the students in classes A and B together is 26 kg. The average weight of all students in classes B and C together is 24 kg. What is the average weight of the students in all the three classes put together. If the average weight of the students in the classes A, B and C are 24 kg, 27 kg and 21 kg respectively.

Answer

To find the average weight of the students in all three classes A, B, and C, we can follow these steps:

### Step 1: Define Variables
Let:
- \( n_A \) = number of students in class A
- \( n_B \) = number of students in class B
- \( n_C \) = number of students in class C

### Step 2: Use Given Averages
From the problem, we know:
- Average weight of A = 24 kg
- Average weight of B = 27 kg
- Average weight of C = 21 kg

### Step 3: Set Up Equations Based on Combined Averages
1. For classes A and B:
\[ \frac{24n_A + 27n_B}{n_A + n_B} = 26 \]
Multiply both sides by \( n_A + n_B \):
\[ 24n_A + 27n_B = 26(n_A + n_B) \]
Simplifying gives:
\[ 24n_A + 27n_B = 26n_A + 26n_B \]
Rearranging:
\[ 2n_B = 2n_A \implies n_A = n_B \]

2. For classes B and C:
\[ \frac{27n_B + 21n_C}{n_B + n_C} = 24 \]
Multiply both sides by \( n_B + n_C \):
\[ 27n_B + 21n_C = 24(n_B + n_C) \]
Simplifying gives:
\[ 27n_B + 21n_C = 24n_B + 24n_C \]
Rearranging:
\[ 3n_B = 3n_C \implies n_B = n_C \]

### Step 4: Determine Ratios
From the above results, we have:
- \( n_A = n_B \)
- \( n_B = n_C \)

Thus, we can conclude:
\[ n_A : n_B : n_C = 1 : 1 : 1 \]

### Step 5: Calculate Total Average
Now, we can calculate the total average weight of all students in classes A, B, and C:
\[ \text{Total Average} = \frac{24n_A + 27n_B + 21n_C}{n_A + n_B + n_C} \]
Substituting \( n_A = n_B = n_C = n \):
\[ \text{Total Average} = \frac{24n + 27n + 21n}{n + n + n} = \frac{72n}{3n} = 24 \text{ kg} \]

### Final Answer
The average weight of the students in all three classes put together is **24 kg**.

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