Find the ratio of the following:
Rs. 8.40 to Rs. 3.15

Answer

To find the ratio of Rs. 8.40 to Rs. 3.15, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Ratio**:
We start by writing the ratio of Rs. 8.40 to Rs. 3.15 as:
\[ \text{Ratio} = \frac{8.40}{3.15} \]

2. **Eliminate the Decimal Points**:
To simplify the calculation, we can eliminate the decimal points. Since both numbers have two decimal places, we can multiply both by 100:
\[ \frac{8.40 \times 100}{3.15 \times 100} = \frac{840}{315} \]

3. **Simplify the Fraction**:
Now we need to simplify the fraction \(\frac{840}{315}\). We can find the greatest common divisor (GCD) of 840 and 315 to simplify it.

4. **Finding GCD**:
We can divide both numbers by their common factors. First, we can divide both by 5:
\[ 840 \div 5 = 168 \quad \text{and} \quad 315 \div 5 = 63 \]
So, we have:
\[ \frac{168}{63} \]

5. **Further Simplification**:
Next, we can divide both 168 and 63 by 3:
\[ 168 \div 3 = 56 \quad \text{and} \quad 63 \div 3 = 21 \]
So, we have:
\[ \frac{56}{21} \]

6. **Final Simplification**:
Finally, we can divide both 56 and 21 by 7:
\[ 56 \div 7 = 8 \quad \text{and} \quad 21 \div 7 = 3 \]
Thus, we get:
\[ \frac{8}{3} \]

7. **Express the Ratio**:
Therefore, the ratio of Rs. 8.40 to Rs. 3.15 is:
\[ 8 : 3 \]

### Final Answer:
The ratio of Rs. 8.40 to Rs. 3.15 is **8 : 3**.

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