Answer :
To find the cost of 12 meters of fabric, we will first calculate the cost per meter of the fabric and then use this to find the total cost for 12 meters.\n\n### Step 1: Convert Mixed Numbers to Improper Fractions\n- Convert [tex]7\frac{1}{3}[/tex] meters to an improper fraction:\n [tex]7\frac{1}{3} = \frac{22}{3}[/tex] \n- Convert [tex]30\frac{1}{4}[/tex] to an improper fraction:\n [tex]30\frac{1}{4} = \frac{121}{4}[/tex] \n\n### Step 2: Find the Cost Per Meter\n- We know that [tex]\frac{22}{3}[/tex] meters costs [tex]\frac{121}{4}[/tex] Rupees.\n- Calculate cost per meter by dividing the cost by the number of meters:\n [tex]\text{Cost per meter} = \frac{121}{4} \div \frac{22}{3}[/tex] \n- To divide fractions, multiply by the reciprocal:\n [tex]\text{Cost per meter} = \frac{121}{4} \times \frac{3}{22}[/tex] \n- Multiply the numerators and the denominators:\n [tex]\text{Cost per meter} = \frac{121 \times 3}{4 \times 22} = \frac{363}{88}[/tex] \n- Simplify the fraction by finding the greatest common divisor (GCD): \n - [tex]\text{GCD}(363, 88) = 11[/tex] \n - [tex]\frac{363}{88} = \frac{33}{8}[/tex] Rupees per meter\n\n### Step 3: Calculate the Cost of 12 Meters\n- Using the simplified cost per meter, [tex]\frac{33}{8}[/tex] Rupees, calculate the cost for 12 meters:\n [tex]\text{Total cost for 12 meters} = 12 \times \frac{33}{8}[/tex] \n- Multiply: \n [tex]\text{Total cost} = \frac{33 \times 12}{8} = \frac{396}{8}[/tex] \n- Simplify the resulting fraction or convert to a decimal for easy interpretation:\n [tex]\frac{396}{8} = 49.5[/tex] Rupees\n\nTherefore, the cost of 12 meters of fabric is ₹49.5.
