Given Information:
- The sum of two numbers is 21.
- The ratio between the two numbers is 2:5.

To find the numbers, we can set up a proportion based on the given ratio. Let's assume the two numbers are 2x and 5x.

Setting up the Proportion:

2x/5x = 2/5

Solving the Proportion:

Cross-multiplying, we have:

2x * 5 = 2 * 5x

10x = 10x

This shows that for any value of x, the equation is true. Therefore, x can be any real number.

Finding the Numbers:

Since we know the sum of the two numbers is 21, we can set up the equation:

2x + 5x = 21

Simplifying,

7x = 21

Dividing both sides of the equation by 7, we get:

x = 3

Now, substituting the value of x back into our assumption, we can find the two numbers:

2x = 2 * 3 = 6

5x = 5 * 3 = 15

Therefore, the two numbers are 6 and 15.

Verifying the Solution:

To verify our solution, we can check if the sum of the numbers is indeed 21:

6 + 15 = 21

Since the sum is correct, we can conclude that the numbers are indeed 6 and 15.

Providing the Options:

Now, let's check the given options:

a) 8 and 13: The sum of these numbers is 8 + 13 = 21. This option is incorrect.

b) 7 and 14: The sum of these numbers is 7 + 14 = 21. This option is incorrect.

c) 6 and 15: The sum of these numbers is 6 + 15 = 21. This option is correct.

d) 12 and 9: The sum of these numbers is 12 + 9 = 21. This option is incorrect.

Conclusion:

The correct option is c) 6 and 15.

6+15=21
the 2 no. are 6 and 15 and there sum is 21