When 35 percent of a number is added to another number the second number increase by its 20 percent .What is the ratio between the second number and the first number ?

Options

A. 4:7
B. 7:4
C. 8:5
D. Data inadequate

Answer

To solve the problem, we need to establish a relationship between the first number (let's call it \( x \)) and the second number (let's call it \( y \)).

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that when 35% of the first number \( x \) is added to the second number \( y \), the result is equal to the second number \( y \) increased by its 20%.

2. **Setting Up the Equation**:
We can express 35% of \( x \) as \( \frac{35}{100}x \) or \( 0.35x \). The increase of \( y \) by 20% can be expressed as \( y + 0.2y = 1.2y \).

Therefore, we can set up the equation:
\[ 0.35x + y = 1.2y \]

3. **Rearranging the Equation**:
To isolate \( x \) and \( y \), we can rearrange the equation:
\[ 0.35x + y - 1.2y = 0 \]
Simplifying this gives:
\[ 0.35x - 0.2y = 0 \]

4. **Expressing \( x \) in Terms of \( y \)**:
We can express \( x \) in terms of \( y \) by rearranging the equation:
\[ 0.35x = 0.2y \]
Dividing both sides by 0.35 gives:
\[ x = \frac{0.2y}{0.35} \]
Simplifying this fraction:
\[ x = \frac{2y}{3.5} = \frac{2y \cdot 2}{3.5 \cdot 2} = \frac{4y}{7} \]

5. **Finding the Ratio**:
Now, we want to find the ratio of \( y \) to \( x \):
\[ \frac{y}{x} = \frac{y}{\frac{4y}{7}} = \frac{y \cdot 7}{4y} = \frac{7}{4} \]

### Final Answer:
The ratio between the second number \( y \) and the first number \( x \) is:
\[ \text{Ratio} = \frac{7}{4} \]