Five friends had lunch in a restaurant. After the lunch, they paid the bill wherein four of them contributed Rs. 20, Rs. 25, Rs. 16 and Rs. 13 towards the bill while the fifth friend contributed Rs. 10 more than the average of the bill paid by each of them. How much (in Rs.) did the fifth friend pay?

Let the amount the fifth friend paid be \( x \).

### Step 1: Total contributions of four friends
The four friends contributed the following amounts:

\[
20 + 25 + 16 + 13 = 74 \, \text{Rs.}
\]

### Step 2: Total amount paid by all five friends
Since the fifth friend contributed \( 10 \, \text{Rs.} \) more than the average of the amount paid by all five friends, the total amount paid by all five friends is:

\[
74 + x \, \text{Rs.}
\]

### Step 3: Expression for the average
The average amount paid by the five friends is:

\[
\frac{74 + x}{5}
\]

According to the problem, the fifth friend paid \( 10 \, \text{Rs.} \) more than this average. Therefore, we have:

\[
x = \frac{74 + x}{5} + 10
\]

### Step 4: Solve the equation
First, multiply both sides of the equation by 5 to eliminate the denominator:

\[
5x = 74 + x + 50
\]

Simplifying:

\[
5x = x + 124
\]

Now subtract \( x \) from both sides:

\[
4x = 124
\]

Solving for \( x \):

\[
x = \frac{124}{4} = 31
\]

### Step 5: Conclusion
The fifth friend paid **Rs. 31**.

Would you like any further details or have questions?

Here are 5 related questions for further practice:
1. If all five friends contributed equal amounts, how much would each have paid?
2. What is the total amount paid by all five friends?
3. What would the average contribution have been without the fifth friend?
4. If one friend could not pay, how much would the others need to contribute to cover the bill?
5. If the total bill had been Rs. 150, how much would the fifth friend need to pay?

**Tip**: Always carefully read word problems to correctly interpret relationships between amounts and averages.

In this problem, four friends contribute Rs. 20, Rs. 25, Rs. 16, and Rs. 13 towards a restaurant bill. The fifth friend pays Rs. 10 more than the average amount paid by all five. Learn how to solve for the fifth friend's contribution using algebraic methods. Suitable for Grades 6-8.

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