Question : 110 is what percent of 200? Or, What percent of 200 is equal to 110?
Correct Answer 55%
Solution & Explanation
Solution
Given number = 200
To find, 110 is what percent of 200?
This question can be written as also
What percent of 200 is equal to 110?
⇒ ?% of 200 = 110
Let ? = m
And the meaning of "of" in mathematics is "Multiplication".
∴ m% of 200 = 110
⇒ m% × 200 = 110
⇒ m/100 × 200 = 110
⇒ 200 m/100 = 110
After cross multiplication, we get
200 m = 110 × 100
After transposing 200 to RHS, we get
m = 110 × 100/200
⇒ m = 11000/200
⇒ m = 55%
Thus, 55% of 200 = 110
Thus, Answer = 55%
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 200 = 110
Here, we have ? = m
a = 200
And, b = 110
Thus, using formula
⇒ m = 110 × 100/200
= 110 × 100/200
= 11000/200 = 55%
Thus, 55% of 200 = 110
Thus, 55% Answer
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