The price of 3 tables and 4 chairs is Rs.3300. With the same money one can buy 2 tables and 10 chairs.If one wants to buy 1 table and 1 chair, how much does he need to pay?

Options

A. 80
B. 140
C. 120
D. 90

Answer

To solve the problem, we need to set up equations based on the information given. Let's denote the price of one table as \( X \) and the price of one chair as \( Y \).

### Step 1: Set up the equations
From the problem, we have two pieces of information:
1. The price of 3 tables and 4 chairs is Rs. 3300.
2. With the same money, one can buy 2 tables and 10 chairs.

We can express these as equations:
1. \( 3X + 4Y = 3300 \) (Equation 1)
2. \( 2X + 10Y = 3300 \) (Equation 2)

### Step 2: Simplify Equation 2
We can simplify Equation 2 by dividing all terms by 2:
\[ X + 5Y = 1650 \quad \text{(Equation 3)} \]

### Step 3: Solve the equations
Now we have two equations:
1. \( 3X + 4Y = 3300 \) (Equation 1)
2. \( X + 5Y = 1650 \) (Equation 3)

We can solve for \( X \) in terms of \( Y \) using Equation 3:
\[ X = 1650 - 5Y \quad \text{(Equation 4)} \]

### Step 4: Substitute Equation 4 into Equation 1
Now substitute Equation 4 into Equation 1:
\[ 3(1650 - 5Y) + 4Y = 3300 \]
Expanding this gives:
\[ 4950 - 15Y + 4Y = 3300 \]
Combining like terms:
\[ 4950 - 11Y = 3300 \]
Now, isolate \( Y \):
\[ -11Y = 3300 - 4950 \]
\[ -11Y = -1650 \]
\[ Y = \frac{-1650}{-11} = 150 \]

### Step 5: Substitute \( Y \) back to find \( X \)
Now that we have \( Y \), substitute it back into Equation 4 to find \( X \):
\[ X = 1650 - 5(150) \]
\[ X = 1650 - 750 = 900 \]

### Step 6: Find the total cost of 1 table and 1 chair
Now we can find the total cost of 1 table and 1 chair:
\[ X + Y = 900 + 150 = 1050 \]

### Final Answer
The cost of 1 table and 1 chair is Rs. 1050.

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