A man buys 4 tables and 5 chairs for ₹1000. Ifhe sells the tables at 10% profit and chairs 20% profit, he earns a profit of ₹ 120. What is the cost of one table?

Options

A. ₹200
B. ₹220
C. ₹240
D. ₹260

Explanation

To solve the problem step by step, we will first establish the variables and equations based on the information given.

### Step 1: Define Variables
Let the cost of one table be \( T \) and the cost of one chair be \( C \).

### Step 2: Set Up the Equation for Total Cost
According to the problem, the man buys 4 tables and 5 chairs for ₹1000. Therefore, we can write the equation:
\[ 4T + 5C = 1000 \]

### Step 3: Calculate Selling Prices
The man sells the tables at a 10% profit and the chairs at a 20% profit. The selling price of one table is:
\[ \text{Selling Price of one table} = T + 0.1T = 1.1T \]
The selling price of one chair is:
\[ \text{Selling Price of one chair} = C + 0.2C = 1.2C \]

### Step 4: Set Up the Equation for Total Selling Price
The total selling price for 4 tables and 5 chairs can be expressed as:
\[ \text{Total Selling Price} = 4(1.1T) + 5(1.2C) \]
This simplifies to:
\[ 4.4T + 6.0C \]

### Step 5: Calculate Total Profit
According to the problem, the total profit earned is ₹120. The profit can be calculated as:
\[ \text{Total Selling Price} - \text{Total Cost} = 120 \]
Substituting the values we have:
\[ (4.4T + 6.0C) - 1000 = 120 \]
This simplifies to:
\[ 4.4T + 6.0C = 1120 \]

### Step 6: Solve the System of Equations
Now we have a system of two equations:
1. \( 4T + 5C = 1000 \) (Equation 1)
2. \( 4.4T + 6C = 1120 \) (Equation 2)

We can solve these equations simultaneously. First, let's multiply Equation 1 by 1.1 to help eliminate \( T \):
\[ 1.1(4T + 5C) = 1.1(1000) \]
This gives us:
\[ 4.4T + 5.5C = 1100 \quad \text{(Equation 3)} \]

### Step 7: Subtract Equation 2 from Equation 3
Now we can subtract Equation 2 from Equation 3:
\[ (4.4T + 5.5C) - (4.4T + 6C) = 1100 - 1120 \]
This simplifies to:
\[ -0.5C = -20 \]
Thus, we find:
\[ C = 40 \]

### Step 8: Substitute \( C \) Back to Find \( T \)
Now substitute \( C = 40 \) back into Equation 1:
\[ 4T + 5(40) = 1000 \]
This simplifies to:
\[ 4T + 200 = 1000 \]
Subtracting 200 from both sides gives:
\[ 4T = 800 \]
Dividing both sides by 4 gives:
\[ T = 200 \]

### Conclusion
The cost of one table is ₹200.