Answer :
To find the cost of 5 1/2 metres of cloth, given that 1 metre costs [tex]₹31 \frac{3}{4}[/tex], we will follow these steps:
Convert Mixed Numbers to Improper Fractions:
The cost of 1 metre is given as [tex]31 \frac{3}{4}[/tex]. First, convert this mixed number to an improper fraction:
[tex]31 \frac{3}{4} = \frac{(31 \times 4) + 3}{4} = \frac{124 + 3}{4} = \frac{127}{4}[/tex]
The length of cloth required is [tex]5 \frac{1}{2}[/tex]. Convert this mixed number to an improper fraction:
[tex]5 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}[/tex]
Calculate Total Cost:
Multiply the cost per metre by the number of metres to find the total cost:
[tex]\text{Total Cost} = \frac{127}{4} \times \frac{11}{2} = \frac{127 \times 11}{4 \times 2} = \frac{1397}{8}[/tex]
Convert Improper Fraction to Mixed Number:
Convert [tex]\frac{1397}{8}[/tex] back to a mixed number:
- Divide 1397 by 8. The quotient is the whole number part, and the remainder is the fractional part.
[tex]1397 \div 8 = 174 \, \text{remainder} \, 5 \quad \Rightarrow \quad 174 \frac{5}{8}[/tex]
Therefore, the cost of 5 1/2 metres of cloth is [tex]₹174 \frac{5}{8}[/tex].