Answer:
To find the cost of 1 meter of cloth, we can set up a proportion based on the given information.
Given:
- Cost of \( \frac{19}{4} \) meters of cloth = \( \frac{171}{2} \) rupees
Let \( x \) be the cost of 1 meter of cloth.
We can set up the proportion:
\[ \frac{\text{Cost of } \frac{19}{4} \text{ meters}}{\text{Cost of } 1 \text{ meter}} = \frac{\frac{171}{2}}{x} \]
\[ \frac{\frac{19}{4}}{1} = \frac{\frac{171}{2}}{x} \]
\[ \frac{19}{4} \times \frac{x}{1} = \frac{171}{2} \]
\[ \frac{19x}{4} = \frac{171}{2} \]
To solve for \( x \), multiply both sides by \( \frac{4}{19} \):
\[ x = \frac{171}{2} \times \frac{4}{19} \]
\[ x = \frac{342}{19} \]
So, the cost of 1 meter of cloth is \( \frac{342}{19} \) rupees.
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