The ratio of two number is 1:2. If 7 is added in both number then ratio become 3:5. Then find these number.

Options

A. `7,14`
B. `21,42`
C. `14,28`
D. `8,40`

Answer

To solve the problem step by step, we will follow the information given in the question.

### Step 1: Define the variables
Let the first number be \( n_1 \) and the second number be \( n_2 \). According to the problem, the ratio of the two numbers is given as \( 1:2 \).

### Step 2: Express the numbers in terms of a variable
Since the ratio of \( n_1 \) to \( n_2 \) is \( 1:2 \), we can express the numbers as:
- \( n_1 = k \)
- \( n_2 = 2k \)
where \( k \) is a common factor.

### Step 3: Set up the equation with the new ratio
The problem states that if 7 is added to both numbers, the new ratio becomes \( 3:5 \). Therefore, we can write the equation as:
\[ \frac{n_1 + 7}{n_2 + 7} = \frac{3}{5} \]

### Step 4: Substitute the expressions for \( n_1 \) and \( n_2 \)
Substituting \( n_1 \) and \( n_2 \) into the equation gives:
\[ \frac{k + 7}{2k + 7} = \frac{3}{5} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 5(k + 7) = 3(2k + 7) \]

### Step 6: Expand both sides
Expanding both sides results in:
\[ 5k + 35 = 6k + 21 \]

### Step 7: Rearrange the equation
Rearranging the equation to isolate \( k \):
\[ 5k - 6k = 21 - 35 \]
This simplifies to:
\[ -k = -14 \]

### Step 8: Solve for \( k \)
Thus, we find:
\[ k = 14 \]

### Step 9: Find the values of \( n_1 \) and \( n_2 \)
Now that we have \( k \), we can find the two numbers:
- \( n_1 = k = 14 \)
- \( n_2 = 2k = 2 \times 14 = 28 \)

### Final Answer
The two numbers are \( 14 \) and \( 28 \).

---