A number is increased by 50% and then the result is decreased by 50%. What is the percent of decrease from the original number to the final number?

Percentage is count of a quantity per 100 quantities. The percent of decrease from the original number to the final number is 25%

How to find the percentage from the total value?

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%

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