 A person buys 5 tables and 9 chairs for 15,400. He sells tables at 10% profit and chairs at 20% profit. If his total profit on selling all the tables and chairs is ₹2,080, what is the cost price of 3 chair

Let's solve this problem step by step.

Let the cost price of one table be \( T \) and the cost price of one chair be \( C \).

### Step 1: Set up the equations based on the given information.

- The total cost for buying 5 tables and 9 chairs is ₹15,400.
  \[
  5T + 9C = 15400 \quad \text{(Equation 1)}
  \]

- The person makes a 10% profit on tables and a 20% profit on chairs. The total profit from selling all tables and chairs is ₹2,080.
  - Profit from selling 5 tables:
    \[
    \text{Profit on 5 tables} = 5 \times \frac{10}{100} \times T = 0.5T
    \]
  - Profit from selling 9 chairs:
    \[
    \text{Profit on 9 chairs} = 9 \times \frac{20}{100} \times C = 1.8C
    \]
  - Total profit:
    \[
    0.5T + 1.8C = 2080 \quad \text{(Equation 2)}
    \]

### Step 2: Solve the system of equations.

We have two equations:
1. \( 5T + 9C = 15400 \)
2. \( 0.5T + 1.8C = 2080 \)

#### Solve Equation 2 for \( T \):
\[
T = \frac{2080 - 1.8C}{0.5}
\]
\[
T = \frac{2080}{0.5} - \frac{1.8C}{0.5}
\]
\[
T = 4160 - 3.6C
\]

#### Substitute \( T = 4160 - 3.6C \) into Equation 1:
\[
5(4160 - 3.6C) + 9C = 15400
\]
\[
20800 - 18C + 9C = 15400
\]
\[
20800 - 9C = 15400
\]
\[
9C = 20800 - 15400
\]
\[
9C = 5400
\]
\[
C = \frac{5400}{9} = 600
\]

### Step 3: Calculate the cost price of 3 chairs.

Since the cost price of one chair \( C \) is ₹600, the cost price of 3 chairs is:
\[
3C = 3 \times 600 = 1800
\]

Thus, the cost price of 3 chairs is ₹1,800.

Would you like to see more details or ask any questions?

---

Here are five related questions:

1. What would be the selling price of one chair if the profit margin is 20%?
2. How would the total cost change if the profit on tables was instead 15%?
3. If the person had bought 7 tables and 9 chairs, what would be the new total cost?
4. How can you find the cost price of the tables from the information given?
5. What would happen to the total profit if the cost of chairs increased by 10%?

**Tip:** When solving equations, carefully isolate variables step by step to avoid errors.

Learn how to calculate the cost price of 3 chairs from a total cost problem involving tables and chairs. Includes step-by-step solution and detailed calculations. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation