Sum of two numbers is 40 and their difference is 4. The ratio of the numbers is

Step-by-Step Solution

To find the ratio of the two numbers, we first need to determine the individual numbers using a system of equations.

1. Define the variables:

   • Let the two numbers be x and y.

2. Set up the equations:

   • Equation 1 (Sum): x + y = 40

   • Equation 2 (Difference): x - y = 4

3. Solve for the variables:

   • Add the two equations: (x + y) + (x - y) = 40 + 4

   • 2x = 44

   • x = 22

   • Substitute x = 22 into Equation 1: 22 + y = 40

   • y = 18

4. Calculate the ratio:

   • The ratio of the numbers is x:y, which is 22:18.

   • Simplify the ratio by dividing both parts by their greatest common divisor, which is 2:

   • 22 / 2 : 18 / 2 = 11:9.