The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:

Options

A. 3500
B. 3700
C. 3800
D. 3900

Answer

To solve the problem step by step, we will define the variables for the prices of chairs and tables, set up equations based on the information given, and then calculate the total price of 12 chairs and 3 tables.

### Step 1: Define Variables
Let:
- \( X \) = price of one chair
- \( Y \) = price of one table

### Step 2: Set Up the First Equation
From the problem, we know that the price of 10 chairs is equal to the price of 4 tables. This gives us the equation:
\[ 10X = 4Y \]
We can simplify this equation to express \( X \) in terms of \( Y \):
\[ X = \frac{4}{10}Y = \frac{2}{5}Y \]

### Step 3: Set Up the Second Equation
We also know that the total price of 15 chairs and 2 tables is Rs. 4000. This gives us another equation:
\[ 15X + 2Y = 4000 \]

### Step 4: Substitute the Value of \( X \)
Now, we will substitute the value of \( X \) from Step 2 into the second equation:
\[ 15\left(\frac{2}{5}Y\right) + 2Y = 4000 \]
This simplifies to:
\[ 6Y + 2Y = 4000 \]
Combining like terms gives:
\[ 8Y = 4000 \]

### Step 5: Solve for \( Y \)
Now, we can solve for \( Y \):
\[ Y = \frac{4000}{8} = 500 \]
So, the price of one table is Rs. 500.

### Step 6: Find the Price of One Chair
Now we will use the value of \( Y \) to find \( X \):
\[ X = \frac{2}{5}Y = \frac{2}{5} \times 500 = 200 \]
So, the price of one chair is Rs. 200.

### Step 7: Calculate the Total Price of 12 Chairs and 3 Tables
Now we can calculate the total price of 12 chairs and 3 tables:
\[ \text{Total Price} = 12X + 3Y \]
Substituting the values of \( X \) and \( Y \):
\[ \text{Total Price} = 12(200) + 3(500) \]
Calculating each term:
\[ = 2400 + 1500 = 3900 \]

### Final Answer
The total price of 12 chairs and 3 tables is Rs. 3900.

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