Let’s solve the problem step by step to find the cost of carpeting [tex]\(\frac{3}{5}\)[/tex] parts of the floor given that the cost to carpet [tex]\(\frac{2}{3}\)[/tex] parts of the floor is Rs 6,000.
First, denote the total cost to carpet the entire floor as [tex]\(x\)[/tex].
1. Assume the cost to carpet [tex]\(\frac{2}{3}\)[/tex] of the floor is Rs 6,000, i.e.,
[tex]\[
\frac{2}{3} \cdot x = 6000
\][/tex]
2. To find the total cost [tex]\(x\)[/tex], solve the equation:
[tex]\[
x = \frac{6000}{\frac{2}{3}}
\][/tex]
3. Dividing by a fraction is the same as multiplying by its reciprocal, so it becomes:
[tex]\[
x = 6000 \times \frac{3}{2}
\][/tex]
4. Perform the multiplication:
[tex]\[
6000 \times \frac{3}{2} = 6000 \times 1.5 = 9000
\][/tex]
5. Hence, the total cost to carpet the entire floor is Rs 9,000.
Next, we need to find the cost to carpet [tex]\(\frac{3}{5}\)[/tex] parts of the floor.
6. Calculate [tex]\(\frac{3}{5}\)[/tex] of the total cost [tex]\(x\)[/tex]:
[tex]\[
\text{Cost to carpet} \frac{3}{5} \text{ of the floor} = \frac{3}{5} \times 9000
\][/tex]
7. Perform the multiplication:
[tex]\[
\frac{3}{5} \times 9000 = 3 \times (9000 \div 5) = 3 \times 1800 = 5400
\][/tex]
Therefore, the cost of carpeting [tex]\(\frac{3}{5}\)[/tex] parts of the floor is Rs 5,400.
