When 30 percent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?

Options

A. `3 : 4`
B. ` 4 : 3`
C. ` 3 : 2`
D. None of these

Answer

To solve the problem step by step, we will define the variables and set up the equation based on the information provided in the question.

### Step-by-Step Solution:

1. **Define the Variables**:
Let the first number be \( a \) and the second number be \( b \).

2. **Understand the Problem**:
According to the question, when 30% of the first number \( a \) is added to the second number \( b \), it results in an increase of \( b \) to its 140%. This can be expressed mathematically.

3. **Set Up the Equation**:
The equation based on the problem statement is:
\[ b + 0.3a = 1.4b \]
Here, \( 0.3a \) represents 30% of \( a \) and \( 1.4b \) represents 140% of \( b \).

4. **Rearrange the Equation**:
Rearranging the equation gives:
\[ 0.3a = 1.4b - b \]
Simplifying the right side:
\[ 0.3a = 0.4b \]

5. **Express \( a \) in Terms of \( b \)**:
To find the ratio \( \frac{a}{b} \), we can rearrange the equation:
\[ \frac{a}{b} = \frac{0.4}{0.3} \]

6. **Simplify the Ratio**:
Simplifying \( \frac{0.4}{0.3} \):
\[ \frac{0.4}{0.3} = \frac{4}{3} \]

7. **Final Ratio**:
Therefore, the ratio of the first number \( a \) to the second number \( b \) is:
\[ a : b = 4 : 3 \]

### Conclusion:
The ratio between the first and the second number is \( 4:3 \).