Question : 65 is what percent of 110? Or, What percent of 110 is equal to 65?
Correct Answer 59.09%
Solution & Explanation
Solution
Given number = 110
To find, 65 is what percent of 110?
This question can be written as also
What percent of 110 is equal to 65?
⇒ ?% of 110 = 65
Let ? = m
And the meaning of "of" in mathematics is "Multiplication".
∴ m% of 110 = 65
⇒ m% × 110 = 65
⇒ m/100 × 110 = 65
⇒ 110 m/100 = 65
After cross multiplication, we get
110 m = 65 × 100
After transposing 110 to RHS, we get
m = 65 × 100/110
⇒ m = 6500/110
⇒ m = 59.09%
Thus, 59.09% of 110 = 65
Thus, Answer = 59.09%
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 110 = 65
Here, we have ? = m
a = 110
And, b = 65
Thus, using formula
⇒ m = 65 × 100/110
= 65 × 100/110
= 6500/110 = 59.09%
Thus, 59.09% of 110 = 65
Thus, 59.09% Answer
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