Eleven friends spent Rs 19 each on a tour and the twelfth friend spent Rs 11 less than the average expenditure of all twelve of them. What is the total money (in Rs) spent by them?

Options

A. 216
B. 227
C. 236
D. 247

Answer

To solve the problem step by step, let's break it down:

**Step 1: Calculate the total expenditure of the first 11 friends.**
Each of the 11 friends spent Rs 19. Therefore, the total expenditure of these friends can be calculated as:
\[ \text{Total expenditure of 11 friends} = 11 \times 19 = 209 \text{ Rs} \]

**Step 2: Define the average expenditure of all 12 friends.**
Let the average expenditure of all 12 friends be denoted as \( A \). The total expenditure of all 12 friends can be expressed as:
\[ \text{Total expenditure of 12 friends} = 12A \]

**Step 3: Determine the expenditure of the 12th friend.**
According to the problem, the 12th friend spent Rs 11 less than the average expenditure of all 12 friends. Therefore, the expenditure of the 12th friend can be expressed as:
\[ \text{Expenditure of 12th friend} = A - 11 \]

**Step 4: Set up the equation.**
The total expenditure of all friends can also be expressed as the sum of the expenditures of the first 11 friends and the 12th friend:
\[ \text{Total expenditure} = \text{Expenditure of 11 friends} + \text{Expenditure of 12th friend} \]
Substituting the known values, we get:
\[ 12A = 209 + (A - 11) \]

**Step 5: Simplify the equation.**
Now, simplify the equation:
\[ 12A = 209 + A - 11 \]
\[ 12A = 198 + A \]

**Step 6: Solve for A.**
Rearranging gives:
\[ 12A - A = 198 \]
\[ 11A = 198 \]
\[ A = \frac{198}{11} = 18 \]

**Step 7: Calculate the total money spent by all friends.**
Now that we have the average expenditure \( A \), we can find the total expenditure of all 12 friends:
\[ \text{Total expenditure} = 12A = 12 \times 18 = 216 \text{ Rs} \]

Thus, the total money spent by all of them is **Rs 216**.

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