9 people went to a hotel for combined dinner. 8 people out of 9 spend Rs. 30 each on dinner . 9th person spend Rs. 20 more than then average of all 9 persons. Find the total expenditure on dinner

Answer

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

### Step 1: Calculate the total expenditure of the first 8 people.
The first 8 people spent Rs. 30 each. Therefore, the total expenditure for these 8 people is:

\[ \text{Total expenditure of 8 people} = 8 \times 30 = 240 \text{ Rs.} \]

**Hint:** Multiply the number of people by the amount each person spent.

### Step 2: Calculate the average expenditure of all 9 people.
Let the average expenditure of all 9 people be \(X\). The total expenditure for all 9 people can be expressed as:

\[ \text{Total expenditure of 9 people} = 9X \]

**Hint:** The total expenditure is the average expenditure multiplied by the number of people.

### Step 3: Determine the expenditure of the 9th person.
According to the problem, the 9th person spent Rs. 20 more than the average expenditure \(X\). Therefore, the expenditure of the 9th person can be expressed as:

\[ \text{Expenditure of 9th person} = X + 20 \]

**Hint:** The 9th person's expenditure is the average plus an additional amount.

### Step 4: Set up the equation for total expenditure.
The total expenditure of all 9 people can also be expressed as the sum of the expenditures of the first 8 people and the 9th person:

\[ 9X = 240 + (X + 20) \]

**Hint:** The total expenditure is the sum of the expenditures of all individuals.

### Step 5: Simplify the equation.
Now, simplify the equation:

\[ 9X = 240 + X + 20 \]
\[ 9X = 240 + 20 + X \]
\[ 9X = 260 + X \]

**Hint:** Combine like terms on the right side of the equation.

### Step 6: Solve for \(X\).
Now, isolate \(X\):

\[ 9X - X = 260 \]
\[ 8X = 260 \]
\[ X = \frac{260}{8} = 32.5 \]

**Hint:** Divide both sides by the coefficient of \(X\) to find its value.

### Step 7: Calculate the total expenditure.
Now that we have the average expenditure \(X\), we can find the total expenditure for all 9 people:

\[ \text{Total expenditure} = 9X = 9 \times 32.5 = 292.5 \text{ Rs.} \]

**Hint:** Multiply the average expenditure by the total number of people to find the total expenditure.

### Final Answer:
The total expenditure on dinner is Rs. 292.5.

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