11 friends went to a hotel and decided to pay the bill amount equally. But 10 of them could pay Rs 60 each, as a result 11th has to pay Rs 50 extra than his share. Find the amount paid by him.

Options

A. Rs 105
B. Rs 110
C. Rs 115
D. Rs 120

Answer

To solve the problem, we need to find out how much the 11th friend paid after the other 10 friends contributed Rs 60 each. Let's break it down step by step.

### Step 1: Define the variables
Let the amount that each friend should ideally pay be \( x \).

### Step 2: Calculate the total bill
Since there are 11 friends, the total bill amount can be expressed as:
\[ \text{Total Bill} = 11x \]

### Step 3: Calculate the contribution of the first 10 friends
The first 10 friends each paid Rs 60. Therefore, their total contribution is:
\[ \text{Total Contribution by 10 friends} = 10 \times 60 = 600 \]

### Step 4: Determine the 11th friend's payment
The 11th friend has to pay Rs 50 more than his share \( x \). Therefore, the amount paid by the 11th friend can be expressed as:
\[ \text{Amount paid by 11th friend} = x + 50 \]

### Step 5: Set up the equation
Since the total bill is equal to the total contributions of all friends, we can set up the equation:
\[ 11x = 600 + (x + 50) \]

### Step 6: Simplify the equation
Now, simplify the equation:
\[ 11x = 600 + x + 50 \]
\[ 11x = 650 + x \]

### Step 7: Solve for \( x \)
Subtract \( x \) from both sides:
\[ 11x - x = 650 \]
\[ 10x = 650 \]
Now, divide both sides by 10:
\[ x = 65 \]

### Step 8: Calculate the amount paid by the 11th friend
Now that we have \( x \), we can find the amount paid by the 11th friend:
\[ \text{Amount paid by 11th friend} = x + 50 = 65 + 50 = 115 \]

### Final Answer
The amount paid by the 11th friend is Rs 115.

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