The ratio of two numbers is 2 : 3. When 4 is added to the numbers, the ratio becomes 7 : 10. The difference between the numbers is:

Correct option is A

Given:

Ratio of two number = 2:3

After adding 4 to number the new ratio = 7:10

Solution:

Let the two numbers be 2x and 3x .

According to the problem, when 4 is added to both numbers, the ratio becomes 7 : 10. Thus, we can set up the following equation:

$$\frac{2x + 4}{3x + 4}$$​ = $$\frac{7}{10}$$​​

Cross-multiplying gives:

10(2x + 4) = 7(3x + 4)

Expanding both sides:

20x + 40 = 21x + 28

Subtracting 20x from both sides:

40 = x + 28

Subtracting 28 from both sides:

x = 12

Thus, the two numbers are

2x = 24

3x = 36

The difference between the numbers is:

36 - 24 = 12