Question : 210 is what percent of 400? Or, What percent of 400 is equal to 210?
Correct Answer 52.5%
Solution & Explanation
Solution
Given number = 400
To find, 210 is what percent of 400?
This question can be written as also
What percent of 400 is equal to 210?
⇒ ?% of 400 = 210
Let ? = m
And the meaning of "of" in mathematics is "Multiplication".
∴ m% of 400 = 210
⇒ m% × 400 = 210
⇒ m/100 × 400 = 210
⇒ 400 m/100 = 210
After cross multiplication, we get
400 m = 210 × 100
After transposing 400 to RHS, we get
m = 210 × 100/400
⇒ m = 21000/400
⇒ m = 52.5%
Thus, 52.5% of 400 = 210
Thus, Answer = 52.5%
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 400 = 210
Here, we have ? = m
a = 400
And, b = 210
Thus, using formula
⇒ m = 210 × 100/400
= 210 × 100/400
= 21000/400 = 52.5%
Thus, 52.5% of 400 = 210
Thus, 52.5% Answer
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