The sum of three consecutive multiples of 11 is 363, find these multiples :

Question

Accepted Answer

To solve the problem of finding three consecutive multiples of 11 whose sum is 363, we can use the following logical reasoning:

1. **Understanding the Problem:**
   - We need to find three consecutive numbers that are multiples of 11.
   - Let these multiples be $11x$, $11(x+1)$, and $11(x+2)$.

2. **Setting Up the Equation:**
   - The sum of these three multiples is given as 363.
   - Therefore, the equation is: 
     $$
     11x + 11(x+1) + 11(x+2) = 363
     $$

3. **Simplifying the Equation:**
   - Combine the terms:
     $$
     11x + 11x + 11 + 11x + 22 = 363
     $$
   - Simplify further:
     $$
     33x + 33 = 363
     $$

4. **Solving for $x$:**
   - Subtract 33 from both sides:
     $$
     33x = 330
     $$
   - Divide by 33:
     $$
     x = 10
     $$

5. **Finding the Multiples:**
   - Substitute $x = 10$ back into the expressions for the multiples:
     - First multiple: $11 \times 10 = 110$
     - Second multiple: $11 \times 11 = 121$
     - Third multiple: $11 \times 12 = 132$

6. **Verification:**
   - Check the sum: $110 + 121 + 132 = 363$, which matches the given sum.

**Explanation of Options:**

- **Option 1: 110, 121, 132**
  - This option correctly lists the three consecutive multiples of 11 that add up to 363, as demonstrated above.

- **Option 2: Wed Nov 22 1933 13:30:00 GMT+0530 (GMT+05:30)**
  - This option is not relevant as it is a date and time, not a set of numbers.

- **Option 3: 121, 132, 143**
  - Although these are consecutive numbers, they are not all multiples of 11. Specifically, 143 is not a multiple of 11.

- **Option 4: 132, 143, 154**
  - These numbers are not consecutive multiples of 11. While 132 is a multiple of 11, 143 is not.

Thus, Option 1 is the correct answer, as it accurately represents the three consecutive multiples of 11 that sum to 363.