Solving the Ratio of Chairs to Tables Purchase

This problem asks us to find the ratio between the number of chairs and the number of tables bought, given the total cost, the total number of items, and the individual costs of a table and a chair.

Setting up the Equations

Let's define the variables:

• Let $t$ represent the number of tables purchased.
• Let $c$ represent the number of chairs purchased.

From the question, we know:

• The total number of items (tables and chairs) is 12. This gives us the first equation: $t + c = 12 \quad (1)$
• The cost of one table is Rs. 50, and the cost of one chair is Rs. 40. The total amount spent is Rs. 500. This gives us the second equation: $50t + 40c = 500 \quad (2)$

Calculating the Number of Tables and Chairs

We need to solve these two equations simultaneously.

From equation (1), we can express $t$ in terms of $c$:

Now, substitute this expression for $t$ into equation (2):

Let's simplify and solve for $c$:

Rearrange the equation to isolate the term with $c$:

Divide by 10 to find the value of $c$:

So, the number of chairs purchased is 10.

Now, use equation (1) to find the number of tables ($t$):

Therefore, the number of tables purchased is 2.

Determining the Ratio

The question asks for the ratio of the numbers of the chairs and tables purchased. This means we need to find the ratio $c:t$.

We found $c = 10$ and $t = 2$.

The ratio is:

To simplify the ratio, divide both numbers by their greatest common divisor, which is 2:

Final Answer

The ratio of the numbers of the chairs and tables purchased is $5:1$.