Percentage is count of a quantity per 100 quantities. The percent of decrease from the original number to the final number is 25%
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Suppose that the number in consideration be N
Then, we get:
Increased number = N + 50% of N
Since 50% of N is: [tex]\dfrac{N}{100} \times 50 = \dfrac{N}{2}[/tex],
thus, the increased number = N + N/2 = 3N/2
Now this result is decreased by 50%
Decreased number = result - 50% of result
Since 50% of result is: [tex]\dfrac{3N/2}{100} \times 50 = \dfrac{3N/2}{2} = \dfrac{3N}{4}[/tex]
Thus, Decreased number = 3N/2 - 3N/4 = 3N/4
Let us suppose that the original number N is decreased y% to get 3N/4(the final number)
Then,
3N/4 = N - y% of N
y% of N is calculated as:
[tex]\dfrac{N}{100} \times y\\[/tex]
Thus, we get:
[tex]\dfrac{3N}{4} = N - \dfrac{N}{100}\times y\\\\\text{Multiplying 100/N on both the sides}\\\\25 \times 3 = 100 - y\\75 = 100 - y\\\\\text{Adding y-75 on both the sides}\\\\75 + y - 75 = 100 - y + y - 75\\\\y = 25[/tex]
Thus, the original number N is decreased y% = 25% to get 3N/4(the final number)
Thus, The percent of decrease from the original number to the final number is 25%
Learn more about percentage here:
https://brainly.com/question/11549320
