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Welcome to our Math lesson on Calculating the Percentage of another Percentage of an Amount, this is the fourth lesson of our suite of math lessons covering the topic of Definition of Percentages, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
In this case, we have to find a compound percentage, which is calculated by multiplying the two percentages and then, the total percentage is used as the term A in the formula of the previous paragraph. Thus, we have
Let's explain this point through an example.
A tailor has to sew 120 dresses in a month. He was able to sew only 80% of this amount and eventually take them to market. However, only 75% of the dresses were sold. How many dresses did the tailor sell during the given month?
The long way would imply calculating how much is 80% of 120 and then, calculate 75% of the new amount obtained. We will use this method as a proof form the short method used below.
In simple words, we have to calculate 75% of 80% of 120. Here, x = 75 and y = 80. Thus, we have
The long way:
The number of dresses the tailor sew (N1) is
The number of dresses sold (N2) is
As you see, the result is the same but the first method is shorter.
Obviously, percentages can also express amounts that are greater than the whole. In such cases, we have the numerator of the corresponding fraction greater than the denominator. Everything else is the same as above.
A researcher planned to read 160 pages in one day but he stayed in library longer and read 184 pages during that day. What percent of the initial goal did he achieve?
We have to calculate how much percent of 160 (the initial plan or the whole) is 184. Taking 184 = A and 160 = B, yields
Hence, 184 represents 115% of 160.
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