Question : 100 is what percent of 180? Or, What percent of 180 is equal to 100?
Correct Answer 55.56%
Solution & Explanation
Solution
Given number = 180
To find, 100 is what percent of 180?
This question can be written as also
What percent of 180 is equal to 100?
⇒ ?% of 180 = 100
Let ? = m
And the meaning of "of" in mathematics is "Multiplication".
∴ m% of 180 = 100
⇒ m% × 180 = 100
⇒ m/100 × 180 = 100
⇒ 180 m/100 = 100
After cross multiplication, we get
180 m = 100 × 100
After transposing 180 to RHS, we get
m = 100 × 100/180
⇒ m = 10000/180
⇒ m = 55.56%
Thus, 55.56% of 180 = 100
Thus, Answer = 55.56%
Shortcut Method to find a number is what percent of other
If we have to find
? % of a = b
Here, let ? = m
Thus, above expression can be written as
m% of a = b
⇒ m/100 × a = b
⇒ m × a/100 = b
After cross multiplication, we get
m × a = b × 100
⇒ m = b × 100/a
Thus, using this formula, we can find a number (a) is what (m) percent of b
In the question, we have to find what percent of 180 = 100
Here, we have ? = m
a = 180
And, b = 100
Thus, using formula
⇒ m = 100 × 100/180
= 100 × 100/180
= 10000/180 = 55.56%
Thus, 55.56% of 180 = 100
Thus, 55.56% Answer
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