Two numbers are in the ratio 3 : 7. If 8 is added to both these numbers, then their ratio becomes 5 : 9. What are these numbers?

Correct option is A

1. Given:

- Two numbers are in the ratio 3 : 7
- When 8 is added to both numbers, the ratio becomes 5 : 9 .
- We need to find the numbers.

2. Concept/Formula Used:

- Let the two numbers be 3x and 7x .
- After adding 8 to both numbers, the new ratio becomes:
$$\frac{3x + 8}{7x + 8} = \frac{5}{9}$$​
- Solve for x by cross-multiplying.

3. Solution:

- From the equation:
9(3x + 8) = 5(7x + 8)
- Expand and simplify:
27x + 72 = 35x + 40
72 - 40 = 35x - 27x
32 = 8x
- Solve for x :
x = 4
- Substitute x = 4 into 3x and 7x :
- First number: 3x = $$3 \times 4$$​ = 12
- Second number: 7x = $$7 \times 4$$​ = 28 

4. Answer:

Option A: 12, 28 .