Ratio = 2:5 Let the numbers be 2x, 5x Then, 2x + 5x = 21 = 7x = 21 Therefore, x = 21/7 = 3 So, the numbers are : 2x = 2 × 3 = 6 And, 5x = 5 × 3 = 15

The problem states that the sum of two numbers is in the ratio 2:5 and the total of these two numbers is 21. We need to find the value of the two numbers.

Let's assume the two numbers are x and y.
According to the problem, the sum of these two numbers is 21, so we can write the equation as:
x + y = 21 ...(1)

The ratio of the two numbers is given as 2:5. This means that the first number is two parts and the second number is five parts of the total ratio. We can represent this as:
x/y = 2/5

To solve this problem, we can use the concept of proportionality. We can cross-multiply the above equation to get:
5x = 2y

Now, we have two equations:
x + y = 21 ...(1)
5x = 2y ...(2)

Solving these two equations simultaneously will give us the values of x and y.

Solving the Equations:
To eliminate one variable, we can multiply equation (1) by 2 and equation (2) by 1. This will give us:
2x + 2y = 42 ...(3)
5x = 2y ...(4)

By subtracting equation (4) from equation (3), we can eliminate the variable 'y':
2x + 2y - 5x = 42 - 2y
-3x = -3y + 42
3x = 3y - 42

Now, we can rewrite the equation in terms of x:
x = (3y - 42)/3
x = y - 14 ...(5)

Substituting the Value of 'x' in terms of 'y' into Equation (1):
We can substitute the value of x from equation (5) into equation (1):
(y - 14) + y = 21
2y - 14 = 21
2y = 21 + 14
2y = 35
y = 35/2
y = 17.5

Substituting the Value of 'y' into Equation (5):
Now, we can substitute the value of y back into equation (5) to find x:
x = 17.5 - 14
x = 3.5

Therefore, the two numbers are 3.5 and 17.5.

Explanation:
- The problem asks to find two numbers whose sum is 21 and in the ratio 2:5.
- We assume the two numbers as x and y.
- We form the equation x + y = 21 based on the sum of the two numbers.
- The ratio of the two numbers is x/y = 2/5.
- By cross-multiplying the ratio equation, we get 5x = 2y.
- We solve the equations simultaneously by eliminating one variable.
- Substituting the value of x in terms of y into equation (1), we find the value of y as 17.5.
- Substituting the value of y into equation (5), we find the value of x as 3.5.
- Thus, the two numbers are 3.5 and 17.5.