Miscellaneous
Percent of a Percent
x% of y = $\frac{x}{100}$ × y
z% of x% of y = $\frac{z}{100}$ × $\frac{x}{100}$ × y
and so on.
You will not that the order in which we apply these percentages is not important:
z% of x% of y = $\frac{z}{100}$ × $\frac{x}{100}$ × y
x% of z% of y = $\frac{x}{100}$ × $\frac{z}{100}$ × y
So, z% of x% of y = x% of z% of y
Q. What is 20% of 50% of 90?
Explanations :
50% of 90 = $\frac{50}{100}$ × 90 = 45
20% of 45 = $\frac{20}{100}$ × 45 = 9
20% of 50% of 90 = 0.2 × 0.5 × 90 = 9
A percentage increase is how many times the original value?
If the percentage increase is 100%, then the new value of something is 2 times the previous given value.
If the percentage increase is 200%, then the new value of something is 3 times the previous given value.
If the percentage increase is 50%, then the new value of something is 1.5 times the previous given value.
So, we can generalize:
If the percentage increase is p%, then the new value of something is (1 + $\frac{p}{100}$) times the old value.
Or we can say that:
If the new value of something is p times the old value, then the percentage increase is (p - 1)100%.
Q. If salary of Mragank is increases by 150%, then his new salary is how many times his earlier salary?
Explanation:
So, New salary = (1 + $\frac{p}{100}$) times the earlier salary = (1 + $\frac{150}{100}$) times the earlier salary = 2.5 times the earlier salary
Q. If X = 5.25 Y, then by how much percent is X more than Y?
Explanation:
So, Percentage increase from Y to X = (p - 1)100% = (5.25 -1)100 = 425%
p times Vs. p times more
Compare these two:
If the new value of something is p times the previous given value, then the percentage increase is (p - 1)100%.
If the new value of something is p times more than the previous given value, then the percentage increase is 100p%.
Q. If price of onion increases to 3 times of its previous value, then what is the percent increase?
Explanation:
If the new value of something is p times the previous given value, then the percentage increase is (p - 1)100%.
So, Percentage increase = (p - 1)100% = (3 - 1)100 = 200%
Q. If price of onion becomes 3 times more than its previous value, then what is the percent increase?
Explanation:
If the new value of something is p times more than the previous given value, then the percentage increase is 100p%.
So, Percentage increase = 100p% = 300%