What is the ratio in ₹ 2.80 and 40 paise?

### Concept & Unit Equivalence To accurately calculate the ratio between two measurements, they must first be converted into identical units. A ratio is unitless and represents the pure relationship between quantities. $$ ₹ 1 = 100 \text{ paise} $$ ### Step-by-Step Solution * Identify the two given quantities: ₹ $2.80$ and $40$ paise. * Convert the larger unit (Rupees) into the smaller unit (paise) to avoid dealing with decimals: $$ 2.80 \times 100 = 280 \text{ paise} $$ * Set up the ratio between the first quantity and the second quantity in their unified measurement: $$ 280 : 40 $$ * Simplify the ratio by dividing both sides by $10$ (dropping the zeros): $$ 28 : 4 $$ * Simplify further by dividing both sides by their greatest common divisor, which is $4$: $$ \frac{28}{4} : \frac{4}{4} = 7 : 1 $$ ### Exam Strategy & Shortcut Instead of full conversion, focus on the core integers $28$ and $4$. The ratio of $28$ to $4$ is $7 : 1$. Since $2.80$ and $0.40$ (representing rupees) are at the exact same decimal magnitude, the integer ratio holds perfectly without extra conversion steps. ### Common Pitfall Trying to form the ratio without converting units, calculating $2.80 : 40$. This produces a vastly incorrect ratio of $0.07 : 1$. Always harmonize units first! ### Final Answer Therefore, the correct answer is **$7 : 1$**.