Direct Proportion Formula
Before going to learn the direct proportion formula, let us recall what is proportion. Proportion definition says that when two ratios are equivalent, they are in proportion. The symbol used to relate the proportions is "∝". Direct proportion is a mathematical comparison between two numbers where the ratio of the two numbers is equal to a constant value. Let us learn the direct proportion formula along with a few solved examples.
What Is the Direct Proportion Formula?
The direction proportion formula says if the quantity y is in direct proportion to quantity x, then we can say:
y = kx
where
 k is the constant of proportionality.
 y increases as x increases.
 y decreases as x decreases.
Let us see the applications of the direction proportion formula in the following section.

Example1: Let us assume that y varies directly with x, and y=30 when x=6. What is the value of y when x=100?
Solution:
Using the direction proportion formula,
y=kx
Substitute the given x and y values, and solve for k.
30=k×6
k=5
The equation is: y=5x
Now, substitute x=100 and find y.
y=5×100 = 500
Answer: The value of y is 500.

Example 2: In a construction company, a supervisor claims that 7 men can complete a task in 42 days. In how many days will 14 men finish the same task?
Solution:
It is given that,
Number of workers according to the supervisor, X = 7
Number of days according to the supervisor, Y = 42
Let the number of workers be, x = 14
Then the number of days will be, y =?
By using these two variables X and x, we can find the constant of proportionality k with the equation X=kx (using the direction proportion formula).
7=k×14
k=7 x 14
k=12
Since this is an inverse proportional situation, as the number of workers increases, the number of days decreases.
Thus, the number of days, Y=ky
y=422
y=21
Answer: It will take 21 days for 14 men to do the same task.