The average of 9 numbers is 30. The average of first 5 numbers is 25 and last 3 numbers is 35, then 6th number is equal to :

Question

Accepted Answer

To solve the problem and justify why Option 3 is the correct answer, let's break down the information given and perform the necessary calculations.

1. **Understanding the Problem:**
   - The average of 9 numbers is 30. This means the sum of all 9 numbers is $9 \times 30 = 270$.
   - The average of the first 5 numbers is 25. Therefore, the sum of the first 5 numbers is $5 \times 25 = 125$.
   - The average of the last 3 numbers is 35. Thus, the sum of the last 3 numbers is $3 \times 35 = 105$.

2. **Finding the 6th Number:**
   - We know the total sum of all 9 numbers is 270.
   - The sum of the first 5 numbers is 125, and the sum of the last 3 numbers is 105.
   - Therefore, the sum of the 6th number can be calculated as follows:
     $$
     \text{Sum of 6th number} = 270 - (125 + 105) = 270 - 230 = 40
     $$

3. **Conclusion:**
   - The 6th number is 40, which corresponds to Option 3.

4. **Explanation of Incorrect Options:**
   - **Option 1 (20):** If the 6th number were 20, the total sum of all numbers would be $125 + 20 + 105 = 250$, which does not match the required total of 270.
   - **Option 2 (30):** If the 6th number were 30, the total sum would be $125 + 30 + 105 = 260$, which is also incorrect.
   - **Option 4 (50):** If the 6th number were 50, the total sum would be $125 + 50 + 105 = 280$, which exceeds the required total.

Therefore, the only correct option that satisfies all conditions is Option 3, where the 6th number is 40.