There are two distinct natural numbers. Each is first increased by 10 then by same percentage as each was increased for the first time. Each number finally results in 72 Find the difference between the numbers.
How to do in simplified way please help
To find the difference between the two numbers, we can first set up an equation based on the given information.
Let's assume the two distinct natural numbers are x and y.
According to the problem, each number is increased by 10 and then increased by the same percentage as it was increased for the first time. We can represent this mathematically as:
x + 10 + p(x + 10) = 72 (Equation 1)
y + 10 + p(y + 10) = 72 (Equation 2)
Here, p represents the percentage increase for both numbers.
Now, we can solve this system of equations to find the values of x, y, and p.
By simplifying Equation 1, we get:
x + 10 + px + 10p = 72
x + px + 20 + 10p = 72
x(1 + p) + 20 + 10p = 72
x(1 + p) = 72 - 20 - 10p
x(1 + p) = 52 - 10p
Similarly, by simplifying Equation 2, we get:
y(1 + p) = 52 - 10p
Since both equations are equal to the same value, we can set them equal to each other:
x(1 + p) = y(1 + p)
Now, we can solve for p:
x = y
Substituting this into the earlier equation, we have:
x(1 + p) = x(1 + p)
x + xp = x + xp
This tells us that p can be any value, as it cancels out on both sides.
So, the percentage increase is not necessary to find the difference between the numbers. We only need to solve for x and y.
To find the difference between x and y, we can subtract one equation from the other:
x(1 + p) = 52 - 10p
y(1 + p) = 52 - 10p
Subtracting equation 2 from equation 1:
x(1 + p) - y(1 + p) = (52 - 10p) - (52 - 10p)
x - y = 0
This means that the difference between x and y is zero.
Therefore, the difference between the two numbers is 0.